How can I get rid of my chronic athletes foot? I always wear socks and wash my shoes regularly, but it seems particularly bad in my work flats

Medication. You have taken the proper steps with good hygeine. You should use a daily antifungal spray or powder, but an oral antifungul for a short period my be the answer.
Change shoes and tx. Get rid of problematic footwear - otherwise wash all laces , soles and footwear in bleach - color safe - if it survives the wash, great - if it doesn't, sorry. Use Lamisil (terbinafine) cream twice daily for two weeks and repeat the wash also sun dry it after the dryer for a few hours.