Today (Sept. 1st) and according to flight tracker sites (like flightradar24), there have been a number of domestic flights. For instance, Vietjet Air, Bangkok Aw and Thai Smile (to Suvanabhumi) and Nok (to Don Meuang) had a single flight from BKK to Phuket vv , whereas Vietjet Air had one to Surat, with another by Nok later this day. So frequency is low and it appears that this morning Nok had a DHC-8 rather than a B737 on a DMK flight to/from Chiang Mai. In the case of Phuket, Thai Lionair and AirAsia are supposed to start on Sept 2nd and 3rd, respectively. So there are some domestic flights now, flying TO Bangkok is presumably easy in terms of restrictions but the other way may be problematic, in particular to Phuket. I would book late as nobody knows what will happen in a few days and getting your money back (and then maybe only just in the form of a voucher which is not really useful) maybe difficult.