Some posters have been approved with 620+ EX scores (Amex seems to be a big EX puller lately). Obviously, the higher the score, the better.
A friendly warning to you though: Many (but not all) people who have fallen victim to Amex AA (CLDs and F/R) have reported a specific commonality -- They obtained an "in" with Amex through Skymiles and then converted to another product and before long.. Bam!... AA!
Of course, I'm not saying this will always be true or that any Amex customer is more likely or less likely than others to be hit with AA. I'm only making an obvervation. Amex has been acting pretty schizo lately so one never knows.
Having said all that, good luck if you choose to apply!
FICO: 8/08 - TU 718; EQ 702; EX 733 (Bonafide 700 club member!) Next goal: 750s across the board!!