Can you do a modified hip flexor stretch without the numbness and tingling (i.e. don’t put your lower leg against a wall, just do the samson stretch)? Strong stretching sensations would be ok (although you probably won’t be able to hold it as long) but there shouldn’t be any nervy pain (burning/tingling/numbness).

With your last paragraph (the bridge test reduces the clicking), I’d say you have a weakness in the glutes/post chain that allows your hip to impinge when flexed. Think hip extensions,bridges progressing to weighted lunges/pistols/etc.