Hello! I undertook this route in May flying on a seperate PG flight no and the bags were interlined without problem both ways and all boarding passes provided at check in. Upon arrival at BKK follow the signs to Phuket transfer and go through immigration + security check. At that point you will be given a sticker for international baggage claim (don't forget you get free lounge access when flying with Bangkok airways). At Phuket you will be directed separately when leaving the plane to the international baggage belts. Enjoy Phuket!