Stomoxys is composed of several species of flies that resemble Musca domestica generally, but the mouthparts are designed for piercing the skin and feeding upon blood. Both the male and female flies take blood meals. The female fly lays eggs in decaying vegetable matter, and the larvae hatch, feed, and pupate in these locations. The adult flies are viscious daytime feeders.
There have been no reports of these flies specifically bothering cats, although they have been found to cause cutaneous lesions at the site of feeding in dogs (White and Bourdeau, 1995). There is every reason to believe that these flies are capable of feeding on cats, and it is likely that there would be reactions at the feeding site.
White SD, Bourdeau P. 1995. Hypersensibilitès aux piqûres de diptères chez les carnivores. Point Vet 27:203-206.