Chris Bradley runs through the legal background, the role of the DSM, and the chances that Chelsea Manning will get what she wants while she is is prison — even if she wants to pay out of her own pocket:
http://lawyerist.com/david-coombs-plans-force-army-pay-chelsea-mannings-sex-change/
The biggest variable is whether the Army will just cave. Politically, it seems like a good option. All it really has to do is say that Manning can get hormone therapy if she wants to pay for it. Seems like a small thing for it to allow.