It doesn't work that way for airline branded Amex's. If you have a BA Amex card, it will give you BA miles; if you have a BMI Amex card, you will get Diamond Club miles, etc. And once you have those miles, it is virtually impossible to transfer them to another programme, at least without losing large chunks of miles on the way.

The link you have posted is only relevant to Amex's own (non-branded) cards, such as the Gold or Platinum card, which earn Amex's Membership Rewards points.

You might want to think about the Amex SPG card though. You earn SPG points not Amex's own Membership Rewards points, but these can then be transferred to a number of different airlines and you get a 25% bonus when transferring 20,000 miles - see here.