I think airflow generally goes out through the wheel, so a complete air dam would reduce brake cooling (by reducing pressure under the car), but a flare pushing air out around a tire shouldn't make much difference.
I first noticed this on one of my cars when I was cleaning the wheels and found grasshopper splats on the inside of the wheel.
Depends a lot on how you're using the brakes, too. If you're hypermiling, you're probably not braking much. On the track, with repeated max-effort braking, opposite situation.
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