Hmmm, off the top of my head:
- Ask what their thoughts are on the WPATH Standards of Care, and how they use them.
- If you think HRT might be important to you, ask what their requirements are before they would be willing to recommend you.
- How long have they been practicing? and what do they specialize in?
- Why do they work with TG's? Is it curiosity or can they relate on a more personal level?
- Research them online and download (might have to pay) any professional papers they've published to get a feel for their focus and beliefs. Alternatively, you can ask them to provide you with copies of any published papers you find, which should be without cost.
- Ask for some book recommendations, then read the books and see if you agree with their thesis and think they are worthy of professional recommendation
Also, do some research to determine the current clinical understanding of certain things which are of interest or concern to you and ask your potential dr about them. For example, when I was looking for my psychologist I asked what their personal opinions were on things like ->-bleeped-<- and bigender identification. I did this because these are things I had put a LOT of thought into and I would be able to feel any disconnect if their answer was something that I truly didn't agree with. If they do give you an answer that you don't expect, ask them to elaborate on their reasoning and you will have a window into their mind.
If they share stories about other patients in an attempt to illustrate some point, pay close attention to how much they are willing to reveal about the person they're talking about. I had one doctor accidentally use another patients real name, needless to day he got crossed of the list.
One more thing, I would suggest meeting each of them in person for an initial consult and asking your questions there - they are usually free. This will give you a subjective experience from which to gauge how comfortable you would be talking to them, something that is hard to do in email and phone calls.
I hope this helps, and good luck!