Loctite works, but if you use the wrong type, it is almost impossible to remove. Instead, I suggest using clear fingernail polish. That is definitely removable, some flute techs use it, and you might even already have some in your house.
1 - Apply fingernail polish sparingly and ONLY on the head of the screw.
2 - That is only a temporary band-aid. If a screw is repeatedly getting loose when playing, there is a problem that needs to be addressed by a flute tech. It might just need to be disassembled, cleaned, and oiled, but the screw or steel hinge rod could also be bent - only your tech can tell for sure.
"Never give a flute player a screwdriver."