I looked into Thai adoption last year. Although my experience is of wanting to become the legal father of my Thai wife's son.
If I remember you correctly, you will want to know the process for 2 foreign parents adopting a Thai/Burmese child.
Can't help you with Burmese.
There is an adoption centre in Bangkok,
Child Adoption Center, 225 Rajvithi Rd, Bangkok 14000.
Tel. 02-2468651, 02-2475084.
A lady at the adoption centre gave us a checklist of about 26 documents we had to produce E.g. birth certificate, criminal record check, letter from biological father and many many more.
The lady said that we must hire a lawyer to oversee the process, on visiting a lawyer to discuss this, he informed me that the process would take 2 years to complete, this is the period of time that the Child Adoption Center will send a representative to our house to observe my relationship with my wife's son before determining if I am a suitable father.
We didn't do it because I had to come back to the UK to go to University.
This website could be helpful to you:
Intercountry Adoption Thailand