zoom K8c BB/CO

Why do you 3b preflop and why not call? What stats do you have on villain?
If you do not give stats or thoughts, I will have to answer with just : Yes...

Why do you want to call K8 OOP?
Indeed, river is bet IMO

We can profittably call K8s as it is a 2.5bb open but it depends on what stats has CO.

call pre because 2010 was 6 years ago. this is too good to bluff. would call K6s vs 3bb open.
XC flop because u have a 2 street hand, u're not making him fold anything with equity anyways (besides some Ax). betting is ok too as long as u don't go bigger than this.
XC turn is pretty much the only play.
river bet is good although it's kind of a nasty spot, can be hard for him to show up with worse hands that call. smaller is probably better i would guess, but can't see how this size is not at least ok. again, go any bigger and u start pwning yourself.

Vs 2.5bb open we can just call this pre. Vs bigger open I would fold as a standard but if you want to play it, then it should be a 3bet.
Cbetting this OTF is not bad but I think check call would work also. When you cbet this, I think you narrow villains range to Kx and draws, maybe some other high pocket pairs call one street. So OTR when flush completes and better Kx are still possible, I would go with check/call so villain could have some bluffs in his range too. Second option is to bet smaller and fold to a raise. Now that you bet so big OTR you will get called only by flushes and higher Kx.