You can get flight training under the Visa Waiver system, if you have another legitimate reason to visit the US.
I visit my daughter once or twice a year and last July, while there on a Visa Waiver, I went to a school and applied to the TSA for permission to undertake flight training. Sent in all the papers, including a scan of the Immigration stamp in my passport and got authority within 2 weeks. The local police even paid for my parking when I went to the station to get fingerprinted.