Traditional sounding flats would be a good choice if there is a specific repertoire that calls for them (which could be the case in some live music spots).
Otherwise, is the flatwound thing due to the idea of not having to replace them for a long time, or for hygienic reasons?
Either way, I would third the D'Addario Chromes suggestion: either the lightest (ECB80, gauges 40-60-75-95) or the "custom-light" set (ECB84, 40-60-80-100).
[There are other products in the "bright flatwound" category, but they're harder to find (Gibson), only come in one gauge (S.I.T.), may not last under the 'wrong' hand chemistries (Rotosound, Ernie Ball Slinky Flatwound), or are as-yet untested long-term (Magma).]
Alternatively, Elixir roundwounds: eternal they aren't , but their peculiar coating process (they coat the entire string, not the outer wrapping wire prior to winding) keeps away crud from the nooks 'n' crannies, as long as the coating lasts.