Amex does not offer secured products. You may be able to get a secured card with another bank such as BofA or Wells Fargo. As long as the BK stays on your record you will unlikely be approved for a non-secured prime card. Rebuilding credit takes a long time - I would start with what you have first, and work your way up.
I got in with AMEX at 7 month CC history today, low AAoA. However, I have no derogs and lates. Young account, several cards, in good standing. I have no idea what my FICO scores are now, but I know they're shot for the next couple months. They were probably just good enough just to tip me in, into primeland (brand-wise) with those guys.