In medical, veterinary and forensic entomology, the ease and affordability of image data acquisition have resulted in whole-image analysis becoming an invaluable approach for species identification. Krawtchouk moment invariants are a classical mathematical transformation that can extract local features from an image, thus allowing subtle species-specific biological variations to be accentuated for subsequent analyses. We extracted Krawtchouk moment invariant features from binarised wing images of 759 male fly specimens from the Calliphoridae, Sarcophagidae and Muscidae families (13 species and a species variant). Subsequently, we trained the Generalized, Unbiased, Interaction Detection and Estimation random forests classifier using linear discriminants derived from these features and inferred the species identity of specimens from the test samples. Fivefold cross-validation results show a 98.56 ± 0.38% (standard error) mean identification accuracy at the family level and a 91.04 ± 1.33% mean identification accuracy at the species level. The mean F1-score of 0.89 ± 0.02 reflects good balance of precision and recall properties of the model. The present study consolidates findings from previous small pilot studies of the usefulness of wing venation patterns for inferring species identities. Thus, the stage is set for the development of a mature data analytic ecosystem for routine computer image-based identification of fly species that are of medical, veterinary and forensic importance.