i wouldn't add flour - given it won't have been cooked off first, it may leave it with a floury taste and ruin the sauce (in my experience)

if we need to thicken it up more, we throw in more grated tasty cheese - as it melts it thickens the sauce

ETA - the floury taste is lost at the start when it's cooked off with the butter - i have found if you add flour to the white sauce without it being cooked off like that, it just doesn't have the right flavour