Does anyone know if the medication Flagyl has any side effect to make birth control ineffective?

No. Despite what you may have heard or read on-line, there is no evidence that Flagyl interferes with birth control pills, and there is no such warning in the package insert. Your prescribing doctor may still tell you to use a back-up form of birth control “just in case”, but there is no evidence that it's necessary. Remember also that no birth control method is 100% effective in preventing pregnancy.