Two pilots can only log flight time in certain circumstances. The key is one regulation: FAR 61.51. It's the universal rule on logging time. What 61.51 does is set up a bunch of "boxes." If you fit in a box, you may log the flight time. If you don't, you can't.

Since you're talking about two qualified pilot, let's assume that there is no instruction involved, so neither of you is logging time based on instruction given or instruction received.

For simplicity, I'm also going to leave out hood work and a safety pilot. Just a plain vanilla VFR or IFR flight in a King Air.

In that case, there are two boxes: the PIC box in 61.51(e) and the SIC box in 61.51(f).

The one who is flying is easy. 61.51(e)(1)(i) - assuming the proper category and class ratings, the sole manipulator of the controls may always log PIC (doesn't matter who is the "real" pilot in command of the flight).

The one who is not flying? 61.51(e) and (f) give you two boxes (you can probably break them down into more, but then this would be much longer ):

Box 1: a private pilot or above may log PIC if "acting as pilot in command of an aircraft on which more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is conducted." 61.51(e)(1)(iii)

Well, your King Air doesn't require two pilots, so the "required under the type certification" is out. And since you're in Part 91, you're not in a operation where more than one pilot is required by "the regulations under which the flight is conducted."

Box 2: Assuming some other qualifications (which your scenario says you have), the non-flying pilot may log SIC time under two conditions. The FAR actually makes it simple since they are related to the conditions for logging PIC. The non-flying pilot may log SIC when "more than one pilot is required under the type certification of the aircraft or the regulations under which the flight is being conducted." 61.51(f)(2) (Sound familiar?)

Well, looks like a no-go. Your King Air doesn't require two pilots so, again, "required under the type certification" is out. And, just like for PIC, nothing in a plain-vanilla Part 91 flight requires two pilots.

Sorry, the flight doesn't fit into a 61.51 box so nothing to log.

Make it into an instructional flight, and instrument practice flight under the hood with a safety pilot or certain types of Part 135 ops, and the answer could change.