In A Nutshell
When recharging a camera flash, you need a battery capable of delivering a high amount of current in a short time. Ideally, you want the batteries with the highest rated capacity.
The highest capacity rechargeable AA batteries are: Ansmann’s 2850 mAh batteries and Powerex’s 2700 mAh batteries. Of these two batteries, Powerex’s 2700 mAh gets the most positive reviews from photographers. It received an average of 4 out 5 stars from 98+ reviewers on Amazon. However, some claim that the Eneloop Pro (2500 mAh) delivers better performance overall. I agree that this battery is probably the best performing rechargeable AA — it is more expensive than the Powerex, however.
If you need batteries that hold their charge for an extended period (3 months or more), you should try the “low self-discharge” batteries — see our review here.