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I'm not sure there's any concrete data what triggers FR with AMEX. As long as you're truthful with your application info especially income, do not violate the TOS of the card, i.e., using Business card to pay yourself and a whole lot of other factors, I don't think you have to worry about it. I got FR'd after my 4th AMEX, the Platinum Card. I signed and sent the 4506-T they requested and all is well after 14 business days.
I must say and I'm sure everyone agrees, it's best if you have a diversified lenders you have credit accounts with. Things change, policies gets updated, etc. Don't set yourself up for failure with limiting to only one lender. Although, I must say, AMEX has been a great part in rebuilding my financial security. I have nothing but positive experience with them.
Congratulations on your AMEX approval!!