I have flown in and out of BKK several times and I have flown Bangkok Air from BKK to Kho Samui, although I have not connected in BKK.
You will need to clear immigration and have you photo taken in BKK before you enter Thailand then travel downstairs and take a short walk to Bangkok Air check-in. You will have to clear security before boarding a bus that takes you to the aircraft. Immigration can take 5 minutes if you are one of the first off the bus and there isn’t a line. Or it can take 1 hour.
It depends on what time you arrive and what other flights arrive just before or at the same time you arrive from ICN.
Bottom line: minimum 1 hour, maximum 2 hours. IMO