You cannot legally do flight training on a visa waiver or class B tourist visa. You need an M1 (vocational study) visa. To get that your flight school needs to issue you with the appropriate visa application form endorsed with their details and verification that you are their potential student.
Separately you need to open a TSA account (Homeland Security) and start the vetting process with them which will include getting fingerprints taken at the US Embassy. The flight school can only let you fly when the TSA approval has come through (although trial flight is exempt).
The reason for two separate processes is that both the State Department (for visas) and Homeland Security (for internal security) have reacted to 9-11 in their own way and they don't bother to integrate their requirements.