So either a doctor, not as skilled as Chopper, took care of King or he did it to himself. Thus, he treated his wounds and recovered for 7 days.
7 days recovery sure is not BS, neither the ancient zoan recovery speed. The manga demonstrated that Ulti and Jack quickly got up again and recovered unless you koed them really hard. But in this case, we saw King and Queen being taken care of, otherwise they would still be highly injured and with no scars, and 7 days of recovery.
Their fight was off panelled. We see the aftermath of Greenbull soloing a bunch of the crew + King and Queen. He could have shown his fire abilities, as well as Queen showing his, and Greenbull would have still kicked their asses regardless. His comment on commanders is another proof that they were no serious threat towards him.