Siamese rescue sometimes has Burmese but they have two lovely cats on their site at the moment.. I would suggest you contact your local CP and if they can homecheck they might be willing to put a branch alert out. Burmese do end up in rescue but you want find kittens.. I had a call the other day about a lady needing to rehome a 10month old Burmese Monty.. but sady she never got back to me with details..
Burmese rescue is the best org to go to and i see they have a few on their website.. Worth ringing and ask to be put on their list. They do rehome all over the country!
BTW i am the person that hopefully guided you here! As you can see there are thousands of unwanted puss cats out there.. and those horrid Pre>>>>>> sites are perhaps not the place to find a puss cat. I hope you found the information i posted to you helpful.. And by the way Welcome to Purrs!