Can I use FFT to interpret accelerometer gestures?
Looking at the data I can't see why you'd want to use FFT for this purpose (I may be wrong though). Lets say you want to detect single or multiple movements based on this data set (which you've attached) the methods I'd be looking at would be


Something on the lines of rate of change of absolute values. First derivative would do nicely I guess.
Wavelet transform maybe? I can't elaborate more on its utility until I know whether you want to know the the position of the peaks or not.


If the only thing you want to detect is single vs multiple oscillation then FFT is, in my opinion, not a very good choice for analysis.