My feet are super flat, and I have plantar fasciitis in both of them. I ADORE
my Birkenstocks - I've collected 40 pairs in the last 15 years. For sneakers, the only ones I can wear without my orthotics are Brooks Ariel. Not terribly cute, but not much is in a 10 wide.
I also like the stapled bottom Sanita clogs. Sanita used to be the supplier for Dansko, but Dansko went to a Chinese supplier a couple years ago and I don't think they're as comfortable as the Sanitas are.
You could also try Orthaheel sandals - they have good arch support, too.
ETA - Doc Martens have NO arch support - they are completely flat inside. You'll have to add some sort of insert if that's what you want to wear.