Can flat feet affect how good you are at sports?

It can: A flatfoot is often not a biomechically sound position. It makes the muscles work harder then when the fooot is in an optimal biomechanical position. The foot in a flatfoot often has to reposition the foot when walking...So yes it can.

Should not: Flat feet can cause some aches and pains, but properly addressed, flat feet should not be a problem.

Yes and no: Flatfeet can give you a disadvantage due to instability in your feet. You may be prone to more injuries as a result. You can still do well in sports provided you have supportive shoes and orthotics to stabilize your feet under exertion.