I'm not showing symptoms of BV or yeast inf, but everytime I have sex my partner gets an itchy rash on shaft & skin. What is it & how do u treat it?

Dermatitis. Is he using a condom? It could be a latex allergy. Are you using a lubricant? It could be an irritant dermatitis due to this. Sometimes, the seminal fluids can be irritating on their own, so maybe he is reacting to your seminal fluid. He can try a condom, if he hasn't been using one, and see if the reaction gets, better, worse, or the same.
May be trichomonas. It may be trichomonas and you need to have your partner tested for that and if positive you both need treatment with Flagyl prescribed by doctor.