I don't think the Flash needs any major reshoots to address the Superman situation. The way the movie end, it raises questions without providing answers and leave to other movies the duty to fill the gaps, and explain wtf is going on.

Kara's backstory and what's up with Clark are left for the Supergirl solo to address. After Kara's movie will be officially announced, it's likely we'll get also casting announcements, and know who's going to play Supes, Cavill or another actor. This is not up to the Flash movie.

Anyway, in the last scene of the Flash, they could insert in post-production a billboard in the background with Superman on it to shut up those speculations around the character. It would cost 0.