How to tell my supervisor that I have severe phobia of flying?
Since it doesn't sound like it's likely that you will be able able to work around it in the immediate future, I think you should schedule a meeting and just have the conversation. Explain your phobia, explain the effects, and explain that you have worked with therapists and that the problem is unresolved.

Treat it like any other health or mental health disability that will affect your ability to carry out the tasks graduate students normally do and make it clear that you will attend conferences by train or bus where possible. There are many questions about health and disability on this site and the consensus generally is that if it will impact your performance, you should bring it up with your supervisor and colleagues as soon as possible.  Since this has already become an issue, you should do that now.