Typically with flat feet, overactive and underactive muscles propagate mechanical imbalances and musculoskeletal abnormalities which lead to multiple foot and ankle injuries. I have first-hand experience, genetically speaking, I am prone to ankle sprains and strains with different severity. Once, I broke my 5th metatarsal due to a minor ankle roll as I was simply walking on an uneven surface (yard).
Overworked and overly tight muscles: PeronealComplex Lat. Gastrocnemius Biceps Femoris TFL
Flat feet plus gravitational pull to the center of gravity can cause a secondary mechanical abnormality. Knee Valgus (knee going inwards) comes with a package of overactive and underactive muscles of its own (2). If not addressed early on, flat feet can eventually have a whole body effect by changing the dynamic of the hip to shoulder to neck. Although no real evidence suggest excessive knee valgus has a direct affect on ankle injuries, but indirectly encourages excess eversion/pronation and inversion/supination which is why they called it a rolled ankle (1).
1) Muscolino, Joseph (2011). Kinesiology: The Skeletal System and Muscle Function (2nd Ed). St. Louis, MI: Elsevier. 2) Clark, M.A., Lucett, S.C., & Sutton, B.G. (Eds.). (2014). Nasm essentials of corrective exercise training (1st ed.). Massachusetts: Jones & Bartlett Learning.