Looks like a brand of Asics, with the arches. Many modern Nike and Adidas running shoes are flat footed. They look a lot like Nikes Aptare SE. But these have slimmer soles
Even though this is a replicas part of the forum. I recommend to go to the
DC Costumes and Props section in "Costumes & Props • Popular Franchises" as this area is for costume replicas that aren't apart of bigger Intellectual Properties like Star Wars, DC, Marvel, etc. You're more likely to get advice over there than over here. Keep on searching