Credit cards usually do not reward awards/FF miles on balance transfer unless under certain promotions. I did took advantage of Citibank's offer last year - FF miles on balance transfer...

First USA used to do with its Southwest credit card but I'm sure about it.

Lastly, it's a good practice have two credit cards; one award card, one low rate card. Use the first card to charge, and tap the second card when you have to carry balance.

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