We present the first flexion-focused gravitational lensing analysis of the first of the strong-lensing “ cosmic telescope ” galaxy clusters , observed as part of the Hubble Frontier Fields initiative . Using HST observations of Abell 2744 ( z = 0.308 ) , we apply a modified Analytic Image Model ( AIM ) technique to measure source galaxy flexion and shear values at a final number density of 82 arcmin ^ { -2 } . By using flexion data alone we are able to identify the primary mass structure aligned along the heart of the cluster in addition to a major substructure peak offset 1.43 ^ { \prime } from the cluster core . We generate two types of nonparametric reconstructions : a flexion aperture mass map , which identified the central potential and substructure peak with mass signal-to-noise of 3.5 \sigma and 2.3 \sigma respectively ; and a convergence map derived directly from the smoothed flexion field . For the primary peak we find a mass of 1.93 \times 10 ^ { 14 } h ^ { -1 } M _ { \odot } within a 45 ” ( 145 h ^ { -1 } kpc ) aperture , and for the western substructure we find a mass of 7.12 \times 10 ^ { 13 } h ^ { -1 } M _ { \odot } within a 25 ” ( 80 h ^ { -1 } kpc ) aperture . The associated peak velocity dispersions were determined to be \sigma _ { v } = 1630 km/s and \sigma _ { v } = 766 km/s , respectively , by fitting nonsingular isothermal sphere profiles to the flexion data . Additionally , we use simultaneous shear measurements to independently reconstruct the broader cluster mass structure , and find that it is unable to reproduce the small-scale structure associated with the flexion reconstructions . Finally , we perform the same analysis on the Abell 2744 parallel sky field , and find no strong phantom signals in the noise reconstructions .