I just stopped trying to wear flats unless they have laces or are booties. That's my solution. I gave into the fact that flats are ten times more uncomfortable to me than anything with a small wedge or heel. That's the reality. A shoe that will not stay on is not comfortable.
Even slipper flats come off of my feet, although I'd do better with those. Oxfords have some potential for me because the laces help to hold them on -- but not the completely flat kind -- they have to have a 3/4 inch heel or so, and then they will be fine.
My personal heel "sweet spot" is about 1.5 inches to 2.5 inches. I can go as low as 3/4" with the right shoe or boot. And as high as 3" with the right one. But lower or higher spell discomfort.
In summer I wear sandals with a wedge -- this solves the problem. Straps plus a teensy bit of height, and I'm more comfy. (By the way, even my flattest sandals cause the same problem for me at the moment...as Mochi and Zapotee can attest -- they watched me flipping out of those in NYC. Grrr!)
By the way, I can't wear heeled pumps or low vamp shoes either, unless they have elastic to keep them on. I am sure there may be a pair or two out there in the world that would stay on, but the only one I've ever found is from Ecco. And it's the only one of theirs that has worked. (Believe me, I try them as they come out every year, hoping against hope...)
I do have one pair of almost flat lower vamp shoes that work pretty well for me. They're a very small wedge 9 West. I have no idea why these ones work better than others I have tried, but on the whole, they stay on, and the wedge means they are not as hard on my feet as those without it.
ETA: I realized after I wrote this that one reason a higher vamped flat is difficult for me personally is that with high arches they can easily be poorly fitting on me. A shoe with laces helps that problem.