No you won't be double dipping; I believe some F-T try to do this before. It looks like most of major airlines' dining programs are run by Dining a La Card www.dalc.com and it will credit the airline you registered last.

The idea has been tried before and it doesn't work.

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"It is not doing the things we like to do, but liking the things we have to do, that makes life blessed." - Goethe