Assume federal permit, not state. . .
Some states like NY and IL require state permit for ESA animals too. Copy this link and proceed.
http://www.fws.gov/forms/3-200-41.pdf
It is self explanatary but you need to highlight the following bullets as best and as thoroughly as possible to speed the process:
-Purpose- acquiring diverse surplus stock from existing breeders. That is, spread the gene pool around. List prospective breeders to acquire from. This is key. Guys like Bill Zovickian, Steve Hall, etc. who are already known to the USFWS biologists who process the paperwork.
-Outline experience with husbandry of other tortoise or turtle species. Highlight past success at propagating or you will need to get mentor letters from other breeders saying they will supervise you. Best to have at least 5 years experience stated.
-Try to get at least one specimen within your state first, but not necessary, to show you already provide husbandry to radiata.
-Advise you will participate in the Bronx Zoo studbook under the direction of Bill Holmstrom.
-Provide photographs and diagram of your setups and facility/yard. Discuss diet, heating, lighting needs, etc.
This will take you about 1/2 day to complete. Send off with $200, then wait 90-120 days. They will send you a form letter advising your permit in in process and assign a tentative permit number to you within 3 weeks. Permit is good for 3 years and renews thereafter for $100 every 3 years. It is VERY rare to not get a permit if you answer these simple questions. Worse case if that USFWS will ask you to clarify certain answers and perhaps delay the permit for an additional 30 days. Otherwise, you will get it no problem. I believe radiata will come off the non-native ESA before too long.
Good luck and get going.