The headword phrase is attested in two syntactical forms: either, as here, the second noun is in the dative (with a singular verb either implicit, as here, or explicit) or else both are nominative with "came together." Either way, we obviously have here an ornithologically specific version of "birds of a feather flock together." See e.g. Diogenes Laertius 9.114.
For the birds in question see LSJ s.v.: the attagas (again alpha 4307) is defined there as a francolin (Tetrao orientalis), the noumenios as "perh. a kind of curlew." Note, however, the anthropomorphic explanation in the paroemiographer Diogenianus (re two collaborating thieves, A. of Thessaly and N. of Corinth).