This is my first build and english isn't my native language, so sorry in advance :]
Read the whole guide and try this or don't comment/vote (not just downvote).
Let's get started:

Kog'Maw was so far my favorite champ, and now Dominion is my new favorite game mode. Combine those two, and you will get dynamite!
Kog is great for dominion, he can win (or double K.O.) most fights 1 vs 1, he has (weak, but at least any) CC, his range is HUGE, and... and.... he is GREAT in early Dominion game with AS runes, 1 lvl in Caustic Spittle and Recurve Bow.
This is pretty simple build - most of damage depends on your Bio-Arcane Barrage combined with Kitae's Bloodrazor and as high as possible Attack Speed. What it offers? The Lightbringer and Frozen Mallet or Entropy (i see 2 ways of doing it here). Will offer slow at pretty long auto attack range, and full target visibility. The Lightbringer with Living Artillery will allow you to do much more than you could so far, enemy could escape me in those alleys of Dominion, with Lightbringer + slow - anyone will be having much harder time against Kog.

Playing as Kog here in dominion is pretty simple - full offense. I know, he is squishy. Well... but he has nice range.
First of all: Dominion is made for offtanks, yes? (i've heard this opinion a lot lately), so, Kog is made for what? That's right - for nuking tanks and offtanks.
Second of all: Kog is slow, but Boots of Swiftness and one Phantom Dancer will give you advantage over some champions. So far i was offensive with Kog in dominion, and have died countless times, but when it comes to escape (if you will know WHEN to escape - map awareness) i had easy times, hit target with ulti and ooze in front of your escape route, then few hits with BAB, again ulti and run, and your enemy is hopefully half hp with you untouched. Ofcourse one good CC and you have to stay and shoot everything you've got because running away with Kog without distance advantage has no point - you just have to stay and fight then.

Cons:
- still slow, Boots and Phantom gives him more speed, but without slowing items Kog would be useless here because most of players have much better escape mechanics.
- squishy, deal with it - you will die ALOT!
- in late game can loose against some hard nukers in 1vs1

Pros:
+ very good in 1vs1 early, and mid game (don't let end game to happen, because you'll be squashed)
+ huge range
+ flexible item build, you can go in magic damage, buy wit's, malady, or get some physical strength buying black cleaver for example. in addition to that kog (not only with this build) will give you mixed damage
+ gives great visibility of target enemy (ulti and Lightbringer), every ally will thank you for it (you'll thank me later :D))
+ huge (and constant) dmg output throughout the whole game.
+ thanks to great range and big dmg output, and ofcourse passive can make room for ally at enemy capture point bringing up to 3 enemies to low hp (or killing one or two) - i recommend Garrison or someone with it for Kog can damage enemy and for his kamikaze passive take good effect and not go to waste.

The choice is simple for me - max out AS, so i can add some nice abilities to Kog later (which is slow, and The Lightbringer debuff), so for me it's 8/19/3, in addition to 8% Attack Speed we have some hp, magic resistance, lousy 2% dodge chance, and buffed Ghost and Exhaust in other trees.

To be honest all choices are good for Dominion, game is so fast, that full off would be very good if it allows you to nuke faster, or full ulti if you ned lower Summoner Spells cooldowns. There's no other thing in Utility tree worth taking for dominion as Kog, maybe apart from faster movement speed, because you won't experience here many OOMs, you won't need longer neutral monster buff durations, experience here runs like crazy without 4 points in masteries, death time is low throughout whole game, and you wont need cooldown reduction as AS Kog'Maw (you be nuking with Bio-Arcane Barrage).

Attack speed, that's it. Best Kog dmg is from Bio-Arcane Barrage combined with high attack speed.
If you look for engame stats (almost 2.5 AS with items i recommend, including Malady as last item), and dmg boost at start , then you will want seals, marks and glyphs with Attack Speed. For quints it's pretty much your choice. Armor penetration, Physical dmg, movement speed or health - those are best choices (last two especially), you can also pick attack speed quints if you want more attack speed at start and then different item.

Remember that chance that you will have full build in Dominion are pretty low, even if you are dominating - you earn cash then, but game is shorter. So just boost your Attack Speed to at least 20% (even marks and glyphs with AS are good) and in other rune slots put whatever you want.

What you want... thats all.
Just be wise, don't pick Promote because it's new - not worth it, but - you can try Garrison, it helps in nuking at enemy tower.
Personally i always have Ghost (movement speed is vital here in Dominion), and one of: Exhaust, Flash, Ignite. Sometimes i pick Revive as second spell, but without 21 points in utility tree i find this spell too useless comparing to others (7,21 sec cooldown with Preservation and Presence of the Master ).

You will need nuke at start, that's why AS runes and Recurve Bow as first item, so for one Caustic Spitlle and two Bio-Arcane Barrage, then take one Void Ooze.
That's most important, after that skill priority is simple:
1st Living Artillery
2nd Bio-Arcane Barrage
3rd Caustic Spittle
4th Void Ooze

As shown above i always use same base for Kog, and pretty much always buy it in same order starting with Recurve Bow, after Bow i buy Boots and after that:
- you can buy Berserker's Greaves if you want faster attack speed at start or Sorcerer's Shoes for increased BAB and Kitae's damage (and ofc other spells), but here in Dominion, like in normal game modes i have found Boots of Swiftness best choice for Kog because he is slow, i mean extra slow, and expecially in this game mode he WILL need speed. You also can buy any defensive boots, like Mercury's Treads or even Ninja Tabi
- must have for Kog, as always. it's damage is lower than Madred's, but still it's like 6th point in Bio-Arcane Barrage
- and so far let's stop at this
- your golden ticket to chasing enemies (along with Phage), and lets not forget, that Eve, Shaco and Twitch (or even Wukong) are pretty popular champions in dominion, so when you see them you can engage with ulti or attack with Lightbringer and don't let them go in stealth.
- more attack speed, and some movement speed.

And now you have some options. First of all now it's time to upgrade Phage, you might want more health and constant slow, or (if you are dominating with Kog) you might want more damage, and not-so-constant slow. Depending on situation pick one:

Most of the times i pick Entropy, even if i'll die 10 times in game i'm still 1st in personal score table due to ~20 kills and some captures.

After slow you will need more attack speed and damage output. But of course it's mine opinion, some will buy survivability items but i think of it that way - it's better to nuke opponent fast and rescue capture point, than play with enemy until someone (ally.... or enemy) will come help. And trust me - Kog here, even at very start is extremely capable of nuking.

Anyways. You might need few things depending on team compositions:
1) More Bio-Arcane Barrage and Kitae's Bloodrazor damage, so your choice will be (ant most of the times it's my choice:


2) More physical damage, but you wont achieve almost 2.5 AS with it, and healing effectiveness is lowered in Dominion, AND Kog doesn't have huge dmg or crit rate for it to be effective enough:


3) Just some additional damage (+ some HP):


IMPORTANT!
Remember, that The Lightbringer is just my pick, and in endgame i do lower dmg than i could with other item with AS and some dmg, but it gives me some advantages which i can then use to win a duel or teamfight. I have killed some enemies when they were visible thanks to Lightbringer and i don't know if i could hit them all with ulti or if mana would let me to.
Any AS/AD or AS/magic dmg build will be good here, you have many options, for example:
Ionic Spark Malady Kitae's Bloodrazor Guinsoo's Rageblade Sword of the Divine - those will give you some magic penetration, full attack speed and additional magic dmg (about 70 every hit, so almost 200 per second)
or more physical dmg focused (still, a rough example, remember that Kog suck at life steal and spell vamp scaling):
Sanguine Blade Entropy Phantom Dancer Zeke's Harbinger Black Cleaver

You won't have any boots at start, so either you will run to the 1st top tower letting others take 2nd on top, or you will go bottom. One way or another just be offensive, get used to exploding after death and learn how to use your passive.
You don't have to wait for anyone to engage in fight, i often ulti 2 enemies and run hitting them with ooze and ulti, and when they will get closer i just focus with Caustic Spittle and BAB on nuker or heavy CCer, in most cases i can kill him (or sometimes both) before i die (or after... love Kog for that :D), if not i at least will hurt them badly (most likely both below 60% hp) and that gives other player from my team possibilities.

Think of yourself as you were a tank, honestly. Well... maybe don't run in the middle of enemy group, but try to be offensive and don't be afraid of loosing duel, if you will do some dmg to enemy others will use that and maybe win.

I won't be talking here what to do in dominion, i will just say that Kog is really mobile champion, and is NOT created for defending towers. Kog catched once is dead Kog, but in other hand Kog is great for being offensive on emeny defending towers, let offtank or tank help you, engage, run, and when they will focus on tank/offtank (you'll be seeing lots of OTs here in dominion) just nuke them and take control over tower.

DON'T FARM IN DOMINION!

DON'T CAMP IN DOMINION!
And... don't wait at capture point for enemy to attack, if he is comin - engage, if no one is attacking you, go away from this tower and go to another! Be mobile!
When low on HP use one of health shrines, or just try to help bigger group of allies, if your hp is on decent level (like 50% and above) just harass the enemy or engage in fight.

Before game starts ask team if they will buy Black Cleaver, Stark's Fervor, or Malady, that means any item that gives buff/debuff that you might want or you might even buy (which would be waste when others will buy it too).

Be mobile, with Boots of Swiftness and Phantom you are fast, use it well.

Try to engage - you always will have advantage in duel/fight when your ulti+ooze with 1-2 BAB hits followed by Caustic Spitlle will land before enemy can hit you. If you are good at kiting you can land about 3 ultis, ooze, caustic and 5-6 hits from BAB, all while running.