Aubrey is most definitely a male name. It's Norman French. I had an Uncle Aubrey, so am very familiar with the name. Unfortunately the poaching has begun, and it has been given to girls in recent years.
Audrey is Old English, definitely female, and has no connection with Aubrey.
Avery makes me think of weighing scales, but that's probably just me! I wouldn't know if an Avery was male or female.