Should work fine as long as the speeds are close, but I would not mix the 8 and 4 gig sticks. You won't see much difference over the 16 gig you would get from the Kingston RAM. Compatibility also depends on the motherboard. Some OEM systems are quite picky with RAM, usually the enthusiast boards accept a lot more varied setup of RAM.
I'd just use the two 8 gig sticks and sell the other 8 and 4.