One thing to be aware of on this topic is that all the major string makers make flats for bass and they sound different from each other in ways. GHS Precision Flats are designed to have a very thumpy, mellow sound with a quick decay to the notes. Sadowsky flats (which I use) are "brighter" in that you hear more overtones like you would on rounds and the sustain is almost like rounds as well. It really depends on the sound you are looking for and why you'd want to use them.
I use flats to have that smooth feel with no finger squeak but I still want punch to the tone. Labella Deep Talkin' flats are a more traditional sounding flat with muted highs and strong fundamentals. D'Addario Chromes are bright to begin with but mellow out.
My choices are limited to Fender and Ernie Ball Flats mostly. If you are lucky, you can find Rotosound or Daddario Chromes (which are limited to 40/100 gauge only)