Aces High! (4,100 XP)

Piggybacking above comment for ease of finding.
GUIDE OF AWESOMENESS:
Edit: Updated strategies and macros after finally deciphering some of the complex mechanics.

EZ MODE:
You will want to keep Flame Shield and Revivify up on you constantly. They can both be refreshed in a short cycle:

- - - - - - - - - - - - - - Repeat: 1, 1, 1, 1, 1, 5, 3 - - - - - - - - - - - - - -

This will refresh Revivify before the 10 second duration is up and will keep near 100% uptime on Flame Shield.
(Note that Flame Shield produces no GCD and can actually be cast quickly "between" 1 and 3.)
(Note that 3 requires a friendly target; you'll either need Auto Self-Cast enabled, OR the target-switching macros below, OR to use your mouse to click on yourself for every 3. Thanks for pointing this out, Cecilkorik!)

This will kill the mob without any thinking required, will survive his nasty Arcane Surge, and will rarely run you out of energy.
Approx. 1min 15sec kill time.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~The End!~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

ADVANCED:

• 
  
  
• These dragons aren't mages. You can cast while faced away, moving, spinning, whatever. This means you can kite the mob away from adds safely while still maintaining your normal rotation.
  .
• 
  
  
• MACRO. You can avoid having to manually switch targets all the time if you are comfortable with macros and pressing different keys (or rebinding 1-5 easily with a bar mod). Replace 3 with
  
/target wyrmrest skytalon
/cast revivify
/targetlasttarget


  and replace 5 with
  
/cast flame shield
/target wyrmrest skytalon
/cast flame shield
/targetlasttarget


  Only 4 requires manually targeting yourself now, and 4 should only be needed if you mess up one of these rotations. :)
  .
• 
  
  
• You can kill the mob faster by using a more difficult rotation:
  
  - - - - - - - - - - - - - - Repeat: 1, 1, {wait}, {wait}, 2, 3 - - - - - - - - - - - - - -
  - - - - - - - - - - - - - - Except for Arcane Surge: 5 - - - - - - - - - - - - - - - - - -
  
  OKAY WHY IS THIS SUPPOSEDLY HARDER?
  
  1. 
     
  2. You have to react quickly with Flame Shield and remember to skip to 3 to get a combo point if you just hit 2. That's not trivial, but it works when you've had practice. (You don't have to shield the whole thing... even just shielding one of the three ticks will allow Revivify to keep you up through the rest.)
  3. 
     
  4. Notice the {wait}s. Don't rush this! If you do, you will find yourself out of energy when you need to hit 5 or refresh 2 or 3. I tried rushing it. I even tried fitting in another 1, 1, 2 before 3. It doesn't work. Yes, you actually do higher dps even though you're not casting half the time!
  5. 
     
  
  
  OKAY WHY IS THIS SUPPOSEDLY FASTER?
  Try it. :)
  This runs off of minimizing energy spent on healing and shielding (way too much spent in the EZ MODE rotation) and using that to fuel stacking 2's, which ramp up to huge dps.
  
  You may want to open with a longer 2 and a longer 3 (1, 1, 1, 1, 1, 2, 3, 3, 3, 3, 3) until you're comfortable with this rotation.
  Approx. 45 sec. kill time.
  .
• 
  
• Confused about combo points?
  - When you use an ability, it places a combo point on the target of the ability and wipes any combo points on other targets. For example, if you cast 1, 1, 1, 1, you should have four combo points on the drake you're killing. If you then use a Revivify, you'll put one combo point on your Wyrmrest Skytalon and wipe all combo points from the mob.
  - Additionally, when you cast something that costs combo points, it checks to see whether you have combo points on your target. This means that, in this example, you would have to be targeting yourself to use that one combo point (hence all the target switching in the macros above). This is a pretty nasty surprise if you're expecting a 5-second Flame Shield and instead you see "That ability requires combo points" and you get nothing. :-/
• 
  

REFERENCE:
1 - Flame Spike 10 Energy. 60 yd range. Instant. Fires a quick jet of fire at your target, causing 943 to 1057 Fire damage. Awards 1 combo point.
2 - Engulf in Flames 50 Energy. 60 yd range. Instant. Launches a blast of flames, igniting your target for 1500 Fire damage every 3 sec. This effect stacks. Lasts longer per combo point:
1 point : 6 seconds
2 points: 10 seconds
3 points: 14 seconds
4 points: 18 seconds
5 points: 22 seconds
3 - Revivify 10 Energy. 60 yd range. Instant. Heals the target for 500 per second. Lasts 10 sec. Awards one combo point. Stacks up to 5 times.
4 - Life Burst 50 Energy. Unlimited range. Instant. Releases a burst of rejuvinating energy, healing friendly targets within 60 yards and increasing the caster's healing done by 50%. Heals for more and lasts longer per combo point:
1 point : 5,000 heal / 5 sec
2 points: 7,500 heal / 10 sec
3 points: 10,000 heal / 15 sec
4 points: 12,500 heal / 20 sec
5 points: 15,000 heal / 25 sec
5 - Flame Shield 25 Energy. Unlimited range. Instant. Surrounds the caster in a shield of flames, reducing all damage taken by 80%. Lasts longer per combo point:
1 point : 2 seconds
2 points: 3 seconds
3 points: 4 seconds
4 points: 5 seconds
5 points: 6 seconds

I had a little trouble on my first two attempts to down one of the enemy drakes. Then I realized that this daily is incredibly easy if you use a particular strategy. As in zero reaction required, zero chance of death, just use a fixed button-mashing pattern and auto-win. Here's how I do it. This method has never failed me so far.

1. Before combat: Target yourself. Stack Revivify five times. You will notice that you can actually build combo points on yourself. Make sure to keep it fully stacked as you search for a target.

2. Find a target near the perimeter of the cloud of drakes. This is important, since you can pick up adds on this daily (just run if you do). Now, making sure the Revivify timer is fresh, hit Flame Shield (while keeping yourself targeted). Now quickly target the drake you want to kill.

3. Mash Flame Spike five times. (button 1, your basic attack)

4. Hit Flame Shield. Note that Flame Shield is not on the GCD. For speed reasons, you'll prob want to hit as soon as Flame Spike #5 lands. (button 5, will block 80% of damage for 6 seconds with five combo points)

5. Revivify. You'll only need to hit it once, since you're just refreshing your five stacks. (button 3, healing DoT for 2500 a second with five stacks)

6. Repeat steps 3-5 until the enemy drake is down to maybe 5-10%, then finish it off by just mashing Flame Spike (assuming you're still near full, which you should be).

If you mash buttons sufficiently fast while using this method, you will have flame shield up about 80% of the time and your five-stacked Revivify will never go down. Using this method, my drake's health never drops below 90k for most fights. If I get unlucky and catch Arcane Surge (deals about 25k damage 3 times) while Flame Shield is down, I only drop to maybe 70k, since my shield will be back up before the second tick. Even in those cases, I usually end the fight at near full health anyway.

Note that the window to do all this and refresh Revivify is rather small. If you mash buttons too slowly or have latency issues, you may end up losing it. I usually only manage to refresh it with maybe ~2 seconds left.

This is probably slightly slower than other methods, but it's still pretty fast, and it requires zero in the way of effort. It's also relatively safe. If you're just interested in an easy rep daily which doesn't require thinking, this makes it one.

The dragon you pilot for this daily is identical to the dragons used in Stage 3 of the Malygos encounter. For this reason, doing this daily is an excellent way to practice Stage 3 Malygos, or to check for UI conflicts with the dragon vehicle UI that may cause your life burst/fire shield to misfire at critical times in the Malygos encounter.