I am going for possibly feasible, or definitely infeasible. If ten samples might be enough we have an answer. If less than a million will never be enough then we have an answer.
Put this down as definitely infeasible, then (at least unless you come up with a very accurate, extremely lossy, very clever mathematical “flattening” of the fingerprint scans.)
Fingerprint scanning is an analog process: it’s essentially a (potentially very poor quality) photograph; according to some website, these may reasonably be as low as 96×96 pixels.
If we take the coarse assumptions that each of these pixels can be reduced to a bit depth of around 3 (that is, around 8 possible brightness levels), that 95% of a 96×96px scan’s pixels are fixed by a finger (or fix-able by your mathematical analysis), and that the finger will only move up to ±10px in each of the X and Z axes, that gives you approximately too many possible images that a given fingerprint might produce.
If you want to find a way to hash “fingerprints”, you will have to find a serious analytic reduction of them based on pivotal attributes, and go about hashing that mathematical characterization of each instead.