Illusionist's bracers and werewolf rulings
Illusionist's Bracers only copy activated abilities. 


  112.3b Activated abilities have a cost and an effect. They are written as “[Cost]: [Effect.] [Activation instructions (if any).]”


Most transform cards, like werewolves and Delver of Secrets, have triggered abilities. Illusionist's Bracers have no effect on them. They will, however, double the activated abilities of Bloodline Keeper, causing it to flip twice when it transforms.

All of the abilities of Mayor of Avabruck and Howlpack Alpha abilities are triggered, so he won't benefit from Illusionist's Bracers unless you give him an activated ability from an outside source.