Obviously the owner or manager of a flying school will want his staff to look reasonably presentable, but it is competence that matters - and competence is generally accompanied by sufficient natural authority that clothing is irrelevant.
Dressing up in airline captain outfits to fly small aeroplanes is silly. As a customer, if all other things were equal, I would choose a school where the instructors dressed normally in place of one where they wore white shirts, and I would generally actively avoid one where the shirts came with gold trimmings.