Mostly only the non touristy gyms provide free training; the more tourist ones will be very hard to get free because they will be viewing you constantly as a tourist; money source; Bank of Bankok ATM...
The gym I'm at now, I showed up and said I wanted to fight for them and would fight twice a month, but not less than once a month, and money was never asked for. It's a very poor gym, but; they've never had a foreign fighter here before.
I had my wife translating for me when I showed up; she told them I left Phuket because I was sick of racism and overpricing for white guys, and thus they treat me like a friend, not a customer.
Of course, the gym is very poor, and I've voluntarily bought a lot of new equipment (2 sets of sparring gloves; 2 sets of shin guards; 2 sets of pad/bag gloves; 1 XXL heavy bag; a new set of pads for the trainer - there is only 1 trainer here). I just thought I should give as much back to the gym as I could. But the only money I've ever given was a share of my fight money; they did not ask for that, either. My manager got a little money from the promoters for producing a fighter, but it was his money, not a cut from my share. But I gave some of the money to my trainer; he was reluctant to take it but I made him. He ended up sharing the money with everyone, including me, anyway (mostly whiskey).
But yeah, if you go to gyms like Tiger or Rawaii in Phuket or something, it may be several months before it's free, and that's only the training, not the room and food.
If you want to be treated like a real Thai pro, you have to go out into the sticks where there are NO OTHER FOREIGNERS about; places where they're not accustomed to ripping whites off, so it does not cross their mind to do so. Even then; if you are getting everything for free, give as much back as you can afford to give, like I did (it's probably better to buy gear than give money; this way the young Thai boys learning Muay Thai will benefit for years to come with your gear; but if you give money it just means your trainers will blow it on whiskey and you'll get no training the next day coz they're all hung over!).