The only spell that I think fits tryndamere is
and
The reason being ghost instead of flash is because you have your spinning slash which will go though 90% of the walls and if ppl decide to follow you with flash you can use ghost and get away. same can be said about chasing. if they flash you can follow with spinning slash and mocking shout to slow then use ghost if necessary.

You don't need ignite on tryn because he hits hard and you will either be killed or they will be killed within 4-5 secs. plus its much better to use spinning slash and hit the final hit.

However the a possible choice for tryn instead of ghost is clense if you know your opponents are going heavy cc.

This is generally for early game hard criting
Tryn has 100 fury = 35% chance crit
Brawlers gloves = 8% chance crit
9.6% chance crit from runes
2% crit from masteries

54.6% crit right of the bat with 100 fury.

however you can switch these with armor pen runes if you feel that you don't need them.
This is generally for those tankier people early game
about 10 armor pen
and
these are to get your ult up ASAP
this will also let you use bloodlust once before rage and right after making rage more effective.
this will also alow you better chasing and escape.

Early game crit so bloodlust will be usable
this is the first item you should aim for since it will give you 18% Lifesteal and 15% crit which will help you a lot. this also makes it so that you will win against other dps carries since you will heal and they will not. and the crit chance is also nice
general movement, this will hold out till you get your second phantom dancer
This is so you have nice hard hitting damage. (the first item you should get for this is)
once you have your executioner + boots + cloak then you can solo dragon if you have a 100 fury.
Crit movement speed and att speed.
self explanatory

another
You then should sell your boots since you will have plenty movement speed from the phantom dancers

you will get either aor aif your opponent decides to get armor. at this point whatever item you got should be able to let you solo baron!

next sell the executioners and pick up whatever you didn't get last time.


note with this build you should be critting about 500-800s even on tanks with armor
and be able to kill any squishies in 3-4 hits.

if your team has an AD tank ask him to buy athis will allow for more Lifesteal giving you 70% life steal meaning each hit will heal you 500-600 health depending on how much armor your opponent has. however even with just 250% lifesteal you should heal 300-400 health per hit. this basiscaly means that if a mage can't do enough dmg on the initial burst to make you rage. you wont rage. this also means that its possible for you to go against another DPS at full health and you at half and heal off of them.

Pros:
Amazing mid-late game carry
Has great escape and chasing ability
Highly sustainable

Cons
Has no hard core CC
Highly item dependent champ
Can be useless if put under continuous Stuns/Suppress

general:
the longer you can delay your ult the more effective and the more dmg you will deal to you opponent. Use your bloodlust up at around half health first before you rage. and by the time you rage and finish you should have bloodlust up again to healyourslef

early game:

When you play tryndamere you should farm extremely well.
if you have over 75% health and have 100 fury you should go for some auto attacks on you opponent if they get too close.

if you are low on health dont go back unless you absolutely have to(no rage). try to recover your health with life steal and bloodlust. this will allow you to continue to gain lvl.

mid-late game:

you should try to be the second person in the fight just so that you can take our some of the opponents ults with your ult saving your teammates from them.

after your rage ends and you run away, go to some nearby monster camp and heal yourself with lifesteal. and then head back into back battle cleaning things up.

You should also try to away take dragon as soon as it spawns. even if you already completed your build most likely your teammates haven't so you will help you entire team. plus by late game you should be able to kill dragon in 3-4 secs so its not that much of a big deal.