A man is flirting in a way that makes you uncomfortable but you don’t want to escalate the situation. How do you proceed?

You proceed any damn way that you want to.

You are not the “escalat-or” in this situation. HE IS. Return awkward to sender (“What makes you think I’d be interested even after I’ve [1] broken eye contact, [2] turned my body away from you, [3] changed the subject, and [4] remained engaged in my own activity until you interrupted me?”), ignore him, tell him you’re not interested or that you have a boyfriend/girlfriend/partner, walk away, throw a drink in his face — whatever gets him away from you satisfactorily and safely.

People know when they’re being given a “no” (even nonverbally and with body language). Harassers only pretend not to pick up on cues so they can continue to push your boundaries with social license. Stamp his social license null, void, and revoked since he’s the bad actor in the situation.