Do anybody know what flight academies allow flight instructors work part time?
I know usually at FBOs you can be p/t employee but I do not know if it can be possible at those busy international flight schools.
I think your best bet would be to call a few you are interested in. I doubt the larger schools need part time CFIs, but they may have a need so just ask.
A smaller flight school would probably be your better bet for part time instructing, but your schedule would have to meet that of your students needs so that can be challenge.