Vatterott College is accredited by the Accrediting Commission of Career Schools and Colleges (ACCSC), in Arlington, Virginia. The Commission is listed by the U.S. Office of Education as a nationally recognized accrediting agency under the provision of Chapter 33, Title 38, U.S. Code and subsequent legislation.
While 866-419-4096 is Synchrony Bank's #3 most popular phone number, it's not the only way to get a hold of their customer care team. You already know from reading above that 800-250-5411 is their best customer phone number overall, and we have put together a comparison of their undefined total ways to contact support for you to look at as well.
They often range from 30 to 90 days. I don't know of a specific timeframe that Synchrony Bank has in place, so you should be able to reapply at any time, if your profile supports it. You could apply now and would very likely get an approval. The time you decide to wait really depends on your goals.