Hi Dave,
A lot of fish can have worms, in reality most of them do and they probably have had them since you purchased them.
Worms left untreated can affect your fishes health overall and could actually shorten/kill then early then need be in the long run if the population is so great it infects organs such as the liver.
The good thing about it is, considering you have a fish that will eat flakes there are products, Jungle brand, Hikari prazi-pro esc.. that can be easily administed which conatin deworming medication.
HB