The Rotation is super simple. Knowing what the abilities do will push you towards a priority. Ill explain priority after the spells are explained.
So Evoker technically has 4 abilities, and a couple CD abilities not including Dragon rage and Deep Breath.
First we need to explain Fire Breath and Eternity Surge. With out taking talents into account this is how it works for them.
Fire Breath has 4 ranks, each rank does the exact same damage except rank 1 does a longer damage over time with a little damage up front while Rank 4 does more damage up front with a shorter damage over time.
Eternity Surge will always hit 1 target with rank 1 and will do the exact same damage spread across 4 targets at rank 4.
With that understood Talents within the talent tree offer you the ability to do more damage based on your fire breath duration. Such as the talent Catalyze which increases Fire Breath damage by 100% tick rate while channeling Disintegrate on a target with fire breath on them.
For this reason Rank 1 is the most important thing to put out. It will hit the same number of targets for fire breath but have a 25ish second duration letting you pummel Disintegrates into it.
Talents like Shattering star increases damage by 30% on a 15second cooldown.
Living flame should only be used as a filler OR during Dragonrage. (will explain a little more in Dragonrage section.
Squall is fantastic and turns you into a fire mage basically. Squall cast timer is the only issue with the spell but there are procs within the tree that allow you to have instant cast and CD resets on Squall.
Dragonrage is your only major CD. Understanding it is where all of your damage will come from. Dragon rage makes your essence burst talent activate 100% of the time on your next living flame or azure strike for 14seconds. it also fires off up to 3 pyres at a target when activated. Essence burst makes your next Essence spending ability free completely. Pyre and disintegrate are your only spenders for this so they are priority during the 14seconds it is active. The problem is Essence burst can only be activated 1 of 2 ways, With Ruby or Azure Essence burst (top talents) and Ruby gives you a 1.4second cast time (if no instant casts are active via fire breath talents).
Azure Strike is instant cast and will 100% grant you Disintegrate stacks in this window. BUT it does minimal damage, so when Living flame has a proc active for instant cast is it the better choice.
AoE situations replace Disintegrate with Pyre and watch the numbers fly.
Deep breath is when all the mobs are grouped in dungeons, not really important but is also a HUGE damage.
Now that the core is explained lets talk Priority.
Shattering star as much as possible before the hard hitting abilities like Eternity surge, a rank 4 Fire breath or Disintegrate.
Maintain Fire Breath damage as much as possible. Rank 1 beats out rank 4 every day of the week unless rank 4 will kill the target.
Keep Eternity Surge on Cooldown, 1 charge for 1 target, 4 charges for 4 targets (talents double this number).
Essence burst Pyre 3targets or Disintegrate 1 target.
Living Flame Instant procs only during Dragonrage otherwise Azurestrike.
Non Essence burst Disintegrates and Pyres
Living Flame hard casting during Dragonrage