I am flat footed. I bought a standing mat (one that is made for a kitchen/workshop) and then got some great shoes (ones intended for nurses and doctors). I did this about 1 week into switching to a standing desk cold turkey. I switched almost 2 years ago now (22 months ago), and sometimes I may go a day sitting at home with my laptop... and I really am happy when I get back to my standing desk at my office the next day.
Proper shoes. Yes! I used to wear lead gowns in operating theaters, adding 20kgs to my existing 100kgs (I'm a smidge and 2m). My feet were absolute agony after each shift. Changing to good shoes and a theatre upgrade that made installed squishy Lino helped a lot (with a big downside - pushing 500kg x-ray gear was not that much easier than pushing it through sand would have been. I effectively plowed the floor every time I more it). Get good shoes!
My wife is a nurse and swears by Dansko shoes and clogs. In fact, go spend a couple minutes at your nearest hospital during shift change and count how many people are wearing them, you'll probably be surprised. They don't have the widest selection however...
Not sure if you can get them everywhere (and the brand name is terrible) Hush Puppies. I am very hard on shoes. I bought a new pair every three months until I found Hush Puppies and I'm now on my second pair that have each lasted over a year. Good brands or bad cheap ones, all lasted weeks or a a few months. I have never had shoes last as long as Hush Puppies before. I've always related it to my weight. I weigh quite a lot and manufacturers seem to make shoes bigger, but not stronger. I go for the shoes they describe as being made for airports, which somehow means they are good for standing (wasn't aware the DHS, border control etc let you keep your shoes on!) www.hushpuppies.com
