If you want a flat that actually has an arch support in it, you're probably out of luck -- or maybe the Cole Haan Nike Air ones (Air Bria?). Your other option is to buy a comfortable flat and put an insole in.
I just went over to my basket of flats and tried a few pairs on. I'm going to sound like a broken record, I'm sure, because these same brands get recommended over and over on TPF. But here are the ones that I tried on, and what I thought in terms of fit/comfort/support. None of the three have any arch support, FWIW -- all have a flat insole. When I refer to "support" below, I'm talking about how the shoe hugs the foot.
Repetto BB: This is a very simple, classic ballet flat (think Brigitte Bardot -- for whom it's named -- or Audrey Hepburn). It has the least support of the three, because the leather is the thinnest/softest/most delicate. It's very comfortable, but I would probably put it at the bottom of the list if you're going to be doing any large amounts of walking. Mine are half a size too large, so I put in Foot Petals heel grips and Dr. Scholl's for Her gel insoles (which actually do have a heel cup and arch support) -- so that makes it a bit more comfortable for extended walking IMO.
Sizing -- order 1/2 size up from US.
Lanvin: Very elegant and simple in appearance. (Mine are suede, and the material is the most buttery, gorgeous suede I've ever encountered. I have a leather pair on order, and assume that the leather is of equally high quality.) Hugs the foot, and provides significantly more support than the Repetto. Feels really wonderful on -- much like a bedroom slipper. Good everyday shoes in my opinion, though I wouldn't necessarily recommend them for heavy walking (e.g. sightseeing). The most expensive of the three by a lot. I've heard that they need to be resoled fairly quickly.
Sizing -- order 1/2 size up from US.
Tory Burch Reva: Trendy, some would argue played out. Difference in comfort between materials -- suede is absolutely wonderful (again, feels like a slipper) and nappa leather is also very soft and comfortable while I find patent painful. The most substantial of the three flats; rubber sole feels "cushiony." This is the one that I'd recommend for substantial amounts of walking (if I were wearing a pair of flats all day sightseeing, for example).
There have been some really terrific deals on Repetto and Reva flats in the sales lately (I've seen them from $50-ish-$80-ish at the low end). For more alternatives, I've also heard good things about Jeffrey Campbell, French Sole (there's currently a sale on at the Garnet Hill catalog site), and the Me Too Nevada flat, and I've personally had great luck with several pairs of Steve Madden flats.
Good luck!