I have the option of flying to BKK via Phuket.

Is there a special immigration checkpoint in Phuket for people with connecting domestic flights?

I have an hour from landing in Phuket until my flight leaves for BKK, so I’m thinking that if I have to go through the regular immigration process, this might be cutting it a bit short.

Depends on which airline you are flying, I think only Thai Airlines and it's partners allow the C.I.Q procedure ---> http://www.suvarnabhumiairport.com/en/1083-domestic-to-international-ciq

You are issued a CIQ sticker on arrival Bankkok, remain on international side, board the Phuket Flight, on arrival Phuket you split off on go through the Immigration channel and Customs.

Depends on which airline you are flying, I think only Thai Airlines and it's partners allow the C.I.Q procedure ---> http://www.suvarnabhumiairport.com/en/1083-domestic-to-international-ciq

You are issued a CIQ sticker on arrival Bankkok, remain on international side, board the Phuket Flight, on arrival Phuket you split off on go through the Immigration channel and Customs.

He's flying into Phuket and then on to Bangkok.

Depends on which airline you are flying, I think only Thai Airlines and it's partners allow the C.I.Q procedure ---> http://www.suvarnabhumiairport.com/en/1083-domestic-to-international-ciq

You are issued a CIQ sticker on arrival Bankkok, remain on international side, board the Phuket Flight, on arrival Phuket you split off on go through the Immigration channel and Customs.

He's flying into Phuket and then on to Bangkok.

Ooops ... not sure it's possible if transit through Phuket.