I accepted a job offer at Company A. My current company offered me a raise and I want to stay. Company A spent 1500 to fly me to train. Can I back out

You say you accepted a job offer, which means you entered into a contract.  What does the contract provide?  While it cannot force you to remain employed by company A, it can restrict your rights to be employed by a competitor.  Even if the contract does not restrict your right to leave company A's employ, I believe that company A would still be able to recover the money it spent training you, because it spent that money in reliance on your commitment to join its employ, although I don't know if company A will want the hassle and expense of suing you over $1,500.