Sure. It's also common for units to swap patches when they train together. Not everyone does it, but every time I've trained internationally at least one person has come to swap patches with me. People like to collect them, usually they'll put them all in a shadowbox when they retire. I know the US sent a lot of training teams to Ukraine around 2017-2018 I believe, it's entirely possible he trained with them and the patch was a gift. There could very well be some 18x American SF guy with a matching Ukrainian flag patch somewhere.

There are pictures of Ukrainians wearing all kinds of goofy patches they've collected from the NATO forces sent to help train them up. There's one floating around with a Ukrainian wearing "Don't Mess With Texas" patch lol.