He does support gun control ? From what I have heard he is right where the SCOTUS is right now on upholding an assault weapons ban. Which is safe because Kennedy knows it will never get enough bipartisan agreement in Congress to be brought to the president.
I’m not sure of what his real feelings are about gun control. But he is a politician trying to run on the Dem ticket so he has to be careful that he doesn’t alienate too many on the left. In any event it doesn’t seem like gun control is a major issue that he intends to push.