I've never had an issue going through security with my peptide (BPC-157), but I keep it in a discreet container that doesn’t draw much attention. I've heard they have been found on other people and confiscated, but no one has ever stopped me. I keep mine refrigerated when not using it, so I have been keeping it in the fridge at home before I travel and then just place it back in the refrigerator after my trip. You could probably carry a small cooler for it or something that keeps it cold and secure, but if you have a prescription label or doctor's note, that can help clarify things if TSA has questions.
I've only travelled with peptides once, but as a testosterone user (TRT) I've traveled with needles and vials of testosterone many times. Even going through places like Dubai with 10 vials and a whack of needles, nobody even batted an eye. I have a legit script for Mounjaro which I bring with me, so if anyone asks I'll just sell it as that. I honestly think putting it all in a bag with needles and stuff is better than hiding a vial in a backpack, if you're saying it's medicine then just go all in. On this last trip with peptides, I brought several pens and put several vials of BAC and raw peptide vials in my testosterone supplies, and put that all through the scanner. Nobody said a thing.
