My first comment on the thread, though I have been following with sympathy.
This comment from @Luisa27 struck me as worthy of attention:
I know you’ve said your friend is totally genuine and only has your best interests at heart, but are you 100% sure this is the case? I’ve been thinking about this a lot and I don’t think I’d behave as she’s is...just my view, but her behaviour seems a bit ‘off’ to me
If I was your good friend I don't think I'd be relaying every event, every nuance to you. The things she is telling you about are torturing you. I think in her place, from the off, I'd have been letting HIM know that I'd seen the eye contact etc - perhaps made a light joke of it just to give him the chance to wake up to himself. I can just about make a case for someone getting an ego boost when there's been a mutual attraction, but that shouldn't be the start of continued flirtation, as this may have turned into.
From DP's point of view, I wonder whether what goes through his head, the logic he applies, is that he knows in his own mind that he is not going to take things any further than office flirting, so what's the harm in indulging in an ego boost when no one's getting hurt [as far as he knows]? He's aware of your concerns but he's not actually DOING anything wrong [in his mind] and won't. The fact that it's disrespectful to you perhaps he squares that what the head doesn't know the heart won't grieve over.
We have to think of desired outcomes in order to develop a strategy, but that's very difficult here. You very wisely said you wouldn't want him to stop all this because he'd been told to stop, or because he knew he'd been found out. It has to be his decision - to wake up to himself and realise this [what he thinks of as] harmless flirtation is just unacceptable when in a committed relationship, and to step back.
So unfortunately OP, I don't think there's anything you can actively DO, apart from decide how long you'll wait for him to wake up to himself.
But do give some thought to why your friend started telling you this stuff, and why she continues.