If we are getting realistic, a pair of wings is always accompanied by a very big pair of chest muscles. Imagine a human with pectorals in proportion to the body as a dove.

With the marvel of modern engineering, they do pretty compact wings able to carry 80kg humans, https://youtu.be/ilx8Ch0eOR4 (Sorry for sharing marketing video)

So in a fantasy world, you could imagine so compact wing part of human body

Is keeping the shirt from flipping inside out a requirement for some reason?
I imagine it would be more like lift the bottom front of the shirt over the top of your head and tuck behind neck so that full chest is exposed, fold arms in to insert hand through arm hole on same side as that arm and then push arms forward to leave shirt hanging off wings, reach behind while leaning back to grab and pull shirt off wings downward in direction of feathers.
Either that or how my wife takes off her bras that don't have clasps, push shoulder straps over and down arms, lift arms out so only chest band is holding on, then push the whole thing down chest and over hips and step out of it. That way it doesn't have to go up and over the breasts.