I have the opposite problem (very high arch), so I'm not sure what flat feet require. I just read
here about flat feet, and the question seems to be, is this a painful condition? Because if it is, you should talk to a podiatrist about it (and it would be worth it--my orthotics helped me immensely with my plantar fasciitis). Shoe inserts designed specifically for flat feet may also help (see
Footsmart). A proper insert can be worn in any cute shoe--in fact, I have to say that my passion for footwear was inspired by my diagnosis with plantar fasciitis. I started looking for cute and comfy shoes with plenty of arch support and lo and behold--I found quite a few. Start experimenting with good brands who also have a reputation for comfort (Taryn Rose, Think, Oh! Shoes, Icon, etc.) Hang around here for more examples!