You making a mistake in terminology, "Flagellar Export Apparatus" is not the same thing as a Flagellum. The FEA is a method for transporting proteins from the cytoplasm to the outside of the cell that can be used for an outside structure and in the case of type III it's also used for excretion. It was given the name "Flagellar" because that's where it was first discovered. Kind of the way Prostaglandins even though they are made throughout the body they were named after the prostate because that's were they were first discovered. So just like you can have Prostaglandins not from the prostate you can have a Flagellar Export Apparatus without a Flagellum.
Actually by bringing up the FEA you are strengtening the case for Evolution because not only was their previous functions/uses for the proteins in the Flagellum their was actually a precursor system for setting them up.
And type III genes is not the same thing as a Type Three secretion system, but we know what it is that we are trying to convey. A comes before B and not the other way around. You forget that the assertion is in the article above and that assertion is .... Called the type III secretory system, this microsyringe enables a bacterium to inject a toxin into its victim (this is how bubonic-plague bacteria kill). This component of the flagellum, then, could have been hanging around a very long time, conferring benefits on any organism that had it, ready to combine with other structures (which also perform functions in primitive living things) into a full-blown, functional flagellum.