In Ultra Rapid Fire, you have 80% cooldown on abilities, activated items and summoner spells. Mana and energy costs have been removed and attack speed bonuses for ranged champs have been doubled. While both teams will most likely have AP heavy, over powered champions, it's champions like blitzcrank that will help set up and sustain your team. Being the tank and drawing agro allows your team to build more AP or AD heavy items and decimate those you pull into your team.

Laning phase (if you decide to have one) is best with another champ who has high burst/would benefit from your pulls.

Obviously there are many other ways to build Blitzcrank in Ultra Rapid Fire, probably even more effective ways, but this is mine and I thought I'd share and get feedback before URF closes.

Dorans items are less useful in URF, though they can still be viable. On Blitzcrank, Amplifying Tome is good because it can upgrade to Iceborn Gauntlet or Zhonya's Hourglass. Warding totem is almost a must simply because it's vital for teleporting and it provides vision; it lets you put out 3 wards.

Unless you're getting slaughtered in lane, I'd try and stay around until I get for a tear of the Goddess and Catalyst the Protector. You want to build the TotG asap to start maxing the Mana stacking, but once you get that, you'll want a Rod of Ages for survivablity. RoA is best built early game, and the extra mana, health and ability power go really well with blitz and URF.
If you are getting slaughtered in game, try building a zhonya's if you need armour or if vsing AP heavy, try Abyssal Scepter if you're laning with an AP champ or Banshee's Veil if you're getting shut down by CC.

Boots of mobility aren't so important right now because with teleport being on a 40 sec CD to towers, it reduces the effectiveness of an out-of-combat movement buff, so feel free to swap them out. I like boots of mobility because it allows me better freedom to move to and from lanes and teamfights though thats personal preference.

If you have any gold left over you can continue upgrading to RoA or Archangels Staff.

ARCHANGELS STAFF
You want to get Archangels to get a Seraphs Embrace. The 60 Ability power adds 60 damage to your grab which is up every 2 seconds and to your ult which is up every 6 seconds. The 250 mana adds 125 shield to your passive as well.
In URF Seraphs Embrace is virtually a free shield that shields 20% of your total mana + 150 that's ready every 24 seconds. Also your passive Mana Barrier gains 500 to its shield as well.
Ideally you'll want to stack and max these even though the active is Unique because each adds 60 AP and 1k Mana but this takes time. Therefore you should always have a TotG or a Archangels Staff Stacking and choosing other items to build while waiting.


ROD OF AGES
The health bonuses help preserve your passive and increases your early game survivabilty. Its Valor's Reward helps stay in lane when leveling and its ability power adds decent damage to your abilities. The mana it provides buffs Seraph's active and your passive. Overall, its a nice all-round item.


MANAMUNE
Your Power Fist (pop) deals 200% of your attack damage to your target, so Manamune's 20 AD isn't too bad. You want a Manamune to upgrade it into Muramana for its 1k mana. Because Seraph's active doesn't stack, having a Muramana gives you the same amount of mana and a unique passive. You don't want to stack Muramana because Seraph's 60 AP is better than 20 AD.