Once upon a time there was a published minimum income requirement for USA-issued Platinum Cards. (There still is in some countries.) However, American Express waived this requirement for existing cardholders, which meant you could apply for any American Express card, and then apply for Platinum. Eventually the requirement was eliminated.

A Platinum Card does not give you any greater spending ability than a Green card. You are paying for benefits, not a larger credit line.

There is no reported method to attract a targeted offer, but it is safe to assume that American Express looks at factors that you cannot easily manipulate such as where you live (zip code), home ownership, educational level, occupation, household income, reported spending on competitors' cards, etc.