We explore the relation between surface magnetic flux of the sun and subsurface flow vorticity for flaring and nonflaring solar active regions. For this purpose, we use a data set consisting of 1009 active regions, including the vorticity measurements of their subsurface flows derived from high-resolution global oscillation network group (GONG) helioseismology data and the corresponding X-ray flare data from the geostationary operation environmental satellite (GOES). Using quantities averaged over the disk passage of active regions, we find that, while there is a considerable spread of the flux and vorticity values, they are more or less linearly related. We distinguish the level of flare activity by X-ray flare class and find that large flux or large vorticity values are sufficient for an active region to produce low-intensity C-class flares. Active regions that produce high-intensity X-class flares are characterized by large values of both flux and vorticity. Active regions that produce M-class flares of intermediate intensity are characterized by large vorticity values. The inclusion of solar subsurface vorticity thus helps to distinguish between flaring and nonflaring active regions.