Despite all the replies given here by a lot of knowledgeable people including SoCal and myself there is still a lot of confusion about the M1 visa and which schools can accept non US students.
* For all training that leads to the issuance of a certificate or rating a M1 visa is required.
Regardless if it is more or less then 18hrs/week. That's a stubborn myth.
* Only SEVIS approved schools can issue the I-20 which is the application form for the visa. Schools DO NOT issue visa, the US embassy/consulate does
As a foreigner (= not a US citizen or Green Card holder) you can only train at a SEVIS approved school.
Here is a link to a list of SEVIS approved schools by state.
Not only aviation you can find all schools here that can accept foreign students. If the flight school you intend to use is not listed here ask them if they have a different business name. If not do not go there regardless of what the school might claim.
No SEVIS approval no foreign students, it's that simple.
International Student and Exchange Visitor Program (SEVP)