Yep, I keep a pair of nitrile gloves readily available so they’re the first thing you find when either of my larger FAK’s is opened. My small kit, not so much; a pair of nitrile gloves would significantly increase the size of the kit and since it’s an owwie kit... Remember, the gloves are mostly to protect the responder from contaminants/bodily fluids. For owwies, I pull a band-aid, hand it to the vic’ in the wrapper and let him/her self treat.