As Delta platinum, you should have one bag for free on KLM light/mini fares anyway. Then, normally, the most significant carrier MSC rule should apply, which is delta transatlantic C bag allowance, even on separate ticket as long as there is through check-in. Now, the problem on the way back is that KLM should through check to SAN but might refuse, and especially, if "the computer says you need to pay XXX" it will be difficult to argues with them at CPH since I am not sure there is much KLM staff around.