We present the first flexion-focused gravitational lensing analysis of the Hubble Frontier Field observations of Abell 2744 (z = 0.308). We apply a modified Analytic Image Model 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 two major substructure peaks, including an NE component that corresponds to previous lensing work and a new peak detection offset 1.43 arcmin from the cluster core towards the east. We generate two types of non-parametric reconstructions: flexion aperture mass maps, which identify central core, E, and NE substructure peaks with mass signal-to-noise contours peaking at 3.5σ, 2.7σ, and 2.3σ, respectively; and convergence maps derived directly from the smoothed flexion field. For the primary peak, we find a mass of (1.62 ± 0.12) x 1014 h–1 M☉ within a 33 arcsec (105 h–1 kpc) aperture, a mass of (2.92 ± 0.26) x 1013 h–1 M☉ within a 16 arcsec (50 h–1 kpc) aperture for the north-eastern substructure, and (8.81 ± 0.52) x 1013 h–1 M☉ within a 25 arcsec (80 h–1 kpc) aperture for the novel eastern substructure.