Sorry if this is answered elsewhere...

If I destroy all of my opponent's ships in a campaign game... Doe all of his squadrons count as being destroyed as well? Because if so, none of them would be eligible for veteran status, and they'd all be scarred... right?

And if so, what if one player Flees the battle by going to hypserspace.... do all of their squadrons become scarred?

It is answered elsewhere, but I'll do so here too:

The advice given by Mr Gernes is that they are only destroyed "for the purposes of Scoring and declaring a Winner"

They are not Scarred unless they are actually destroyed in the game... This includes if all ships Hyperspace out.