Context. We propose a novel methodology to identity flows in the solar atmosphere and classify their velocities as either supersonic, subsonic, or sonic. Aims. The proposed methodology consists of three parts. First, an algorithm is applied to the Solar Dynamics Observatory (SDO) image data to locate and track flows, resulting in the trajectory of each flow over time. Thereafter, the differential emission measure inversion method is applied to six Atmospheric Imaging Assembly (AIA) channels along the trajectory of each flow in order to estimate its background temperature and sound speed. Finally, we classify each flow as supersonic, subsonic, or sonic by performing simultaneous hypothesis tests on whether the velocity bounds of the flow are larger, smaller, or equal to the background sound speed. Methods. The proposed methodology was applied to the SDO image data from the 171Å spectral line for the date 6 March 2012 from 12:22:00 to 12:35:00 and again for the date 9 March 2012 from 03:00:00 to 03:24:00. Eighteen plasma flows were detected, 11 of which were classified as supersonic, 3 as subsonic, and 3 as sonic at a 70% level of significance. Out of all these cases, 2 flows cannot be strictly ascribed to one of the respective categories as they change from the subsonic state to supersonic and vice versa. We labeled them as a subclass of transonic flows. Results. The proposed methodology provides an automatic and scalable solution to identify small-scale flows and to classify their velocities as either supersonic, subsonic, or sonic. It can be used to characterize the physical properties of the solar atmosphere. Conclusions. We identified and classified small-scale flow patterns in flaring loops. The results show that the flows can be classified into four classes: sub-, super-, trans-sonic, and sonic. The flows occur in the complex structure of the active region magnetic loops. The detected flows from AIA images can be analyzed in combination with the other high-resolution observational data, such as Hi-C 2.1 data, and be used for the development of theories describing the physical conditions responsible for the formation of flow patterns.