Is there a special market for thai boxing stuff (gloves, etc) in Bangkok/Phuket?

If you're going to training at a Muay Thai camp, they often sell equipment at the camps or I'm sure could tell you the best place to shop. There are also a large number of sporting good shops just past National Stadium off Rama I Rd. in the opposite direction of the MBK Mall, some shops there specialize in Muay Thai equipment. Otherwise, if you're just looking for souvenir type of shorts and gloves, you can buy those types of things at some of the shops on Sukhumvit, just above Soi 3. Someone at your hotel should also be able to tell you a good place to go for what you're looking for.