Because advising people to do otherwise in situations like this is like advising them to do brain surgery on themselves. I feel I know a lot about the law, but the most important thing I know about it is how important it is to know when to get a lawyer. In this case, if the OP really wants to know his legal rights, he's going to need a real lawyer.
$400 isn't brain surgery, and suggesting hiring a lawyer for that amount is crazy.
This is a perfect small claims situation. I don't know if the flight school is entitled to keep the OP's money, but solving issues like this is one of the government services for which we pay taxes.
The OP needs to check with the JP in the Flight School's location for the exact procedure, but in general most small claims go like this:
1) Write a certified letter with return receipt to the school that ripped off the $400. Explain in civil terms why the OP feels he or she is entitled to a refund. Inform the school that the OP will file a claim in small claims court if an amicable solution cannot be reached.
In most small claims venues you can only recover actual damages, not 'pain and suffering' types of things.
2) If the school ignores the letter, or refuses to refund the money go see the clerk of the small claims court that has jurisdiction over the school's location, file a claim, pay a fee, schedule a court date.
I've filed a few small claims actions for small amounts like this in my life. Not one has ever actually gone to court.
Keep in mind that in most states a corporation must be represented by an attorney, and most small business are corporations of one sort or another.
For this reason it will be cheaper for the flight school to pay the $400 to the ripped off student than it would be to pay the attorney $400 to show up in court where the school might or might not prevail.
OP, don't let the flight school rip you off!
Edited to add:
Here is how we do it where I live.