Unless battery life is significantly impacted (say, 25% less life), this description applies. If it is significantly impacted, your flash card may have problems.
It's important to know what is going on inside a DS game card and a flash card. The DS game card has a ROM chip and probably a Flash memory chip for saves. The ROM really only uses power when it is read, and this is very small. The flash is only used when saving and loading. A flash card on the other hand, has a microcontroller, uSD card driver and the uSD card itself to run. The microcontroller is necessary to read the uSD card and output the signals that the DS expects. As a result, it is running all the time.
TrolleyDave is correct in saying that the uSD reader contributes to power drain, but most comes from the microcontroller. It's just a small disadvantage to using Flash cards.