Apple is all about secrets. Without paying to join their certified MFi program, which has a Draconian Non-Disclosure Agreement on pretty much everything, you can't know for sure. Unless a person in the MFi program leaks or shares that information, but if Apple catches them, oh boy are they in a world of legal hurt.
That said, there is some anecdotal information. From https://apple.stackexchange.com/questions/24554/how-much-current-power-can-be-drawn-from-iphone-30-pin-connector mainly the user tofustew's answer:
Somewhere around 160 mA.
Kineteka sells a 30 pin breakout board and pin 18 supplies the 3.3 volts. I just connected a 500 ohm pot between pin 18 and ground and lowered the resistance while measuring the current. It tops out around 160 mA. Try it!
This is for the 30 pin connector, using the ipod/iphone standard. Things have changed with the iphone/ipad, they require more authentication recently. The Camera Connection kit used to be able to request more current (100mA) before iOS 4.2, now it can only request 20mA. Essentially, Apple broke it to spite people using the kits for non-apple approved stuff like keyboards and flash drives.
And the 8 pin Lightning connector? Forget about it. All the pins are multi-function, you won't get any power until the cable authenticates. But it still has the camera connection kit, with the same current limit (20~100mA)