Reddit mentions of Avia (Brown Shoes Men's AVI-Walker, Black/Grey/Yellow, 11 M US

I think a good way to go about it is go to your local shoe store or wherever you buy shoes and try on different brands of walking shoes. Should be relatively easy to find one in the exact style and color you want.

I have flat feet as well and usually arch support is the most important feature in a shoe that I will be wearing and standing/walking with for more than a few hours.

This is the pair I wear at work standing for up to 8 hours. The non-slip and oil resistant sole is also a useful feature IMO.

You might also want to consider shoe inserts, but I don't have any experience with those.

Depending on how serious your condition is, especially if there is considerable pain from standing or walking for long periods of time you might even want to see a podiatrist or other professional. Hope this helped!