Slowplaying has a couple of criterias that need to be fulfilled in order to be correct. Among these are that the pot needs to be small (yup!) and that it's likely that someone may improve to a second-best hand (nope!). We're not risking someone improving to a second best hand, we're risking someone improving to a best hand, and that's not good.
Besides, we just checked our option in the BB. No one is going to give us credit for a monster if we bet out, so deception is on our side here. However, and this is important, if I'm on the button with a flush draw and you accidently flash your cards to me in the BB, I would still call a pot sized bet. If a third club falls on the turn, you will still pay me off enough to have warranted the $6 I put in on this flop. Sure, you could do a ridiculous overbet (all-in, or so) and I'd have to toss my 9c8c, but don't kid yourself into thinking that a flush draw would be smart to fold to even a pot sized bet on this flop. No, we should bet, but it's primarily in order to get worse hands to call, not to fold out flush draws. Giving free cards suck but not because someone will draw out on us for free, but because we fail to get paid all the times that they miss.
Bet. $4-6 seems like a good amount; flush draws and weak aces will call; strong aces and two-pair+ hands will even raise. Good for us.