Can falconers gift their birds feathers? I've been looking for the laws around that topic but I can't find anything.
Yes, but only to individuals or organizations with valid permits to keep them. The official word from the Federal Falconry Regulations text is:
ii) You may donate feathers from a falconry bird, except golden eagle feathers, to any person or institution with a valid permit to have them, or to anyone exempt from the permit requirement under §21.12. (which is here)
So basically you can only legally own bird of prey feathers if you are a member of a federally recognized Native American Tribe, a licensed falconer, or a member of a school or organization that has the valid permits to legally possess raptor feathers.
Quick sketch of a Deinonychus Antirrhopus resting in a dead tree. I did this while watching a speedsketch by the incredibly talented Joschua Knüppe on youtube, and I would highly recommend checking out his work.