Miniature flow sensor for detecting breath movement
You could try using a thermistor that is powered sufficiently to raise its temperature to significantly above "breath" temperature - the air passing will have a cooling effect and this will be seen as a change in resistance.

Use a constant current feed and a positive temperature coefficient thermistor or RTD. If it's a 100 ohm device it'll be about 169 ohms at 100degC and you'll need to experiment a little bit with the current feed to get it in the vicinity of (maybe 80degC).

As colder air crosses the thermistor it will cool and lower its resistance - this will result in a change of voltage across the device's terminals and this could be detected by a simple comparator circuit with a little hysteresis and a low pass filter on the reference input. Here's an idea: -



Current into the thermistor is controlled by R and Vx - current is \$\dfrac{V_X}{R}\$

Vx can be tweaked by altering the potential divider on the op-amp on the left.