You remember that episode of Batman where Batman disappears and Superman has to cover for him, and he does Batman's voice and gets in costume? Well
Now, think about a situation in which, for some reason, Bruce has to appear as Bruce Wayne, or perhaps suspicions of him being the Batman are really strong, and he needs Clark to be Batman for him. Clark is way too good at impersonating The Batman. Not that Bruce says it.
It feels a little uncanny even if this is exactly what he was hoping for...
They end up interacting for whatever reason and maybe at the end of the emergency, to have a little bit of fun, one of them starts to flirt with the other. Aggressively, "in character"
Furthering the Bruce/Batman rumors
Like, Bruce being all over Clark, making him nervous and playfully calling him "Batman" in a half mocking half flirty way that drives Clark insaaaane. Is this a test??? Will he be in trouble if he responds??? Could reciprocating count as being in character??? Everyone knows Batman has had a lot of flings! Should he get back at Bruce??? Now?? Later???
Or perhaps
Clark starts saying, embarrassing, flirty, and somewhat romantic things he thinks would sound way more hilarious if Batman were to say them. With a flat tone and a pokerface
He's either being very annoying to Bruce for ruining his reputation, or he's actually a smooth talker that leaves Bruce kinda speechless?? And WHAT ON EARTH IS HE SUPPOSED TO SAY to thOSE ADVANCES??? Bruce Wayne would, of course, respond in kind!!! Is Clark teasing him? Making fun of him?? Should he get back at Clark??? Bc he's definitely earning consequences, two can play that game after all...
