Sure, you could add flow arrows to a pipe tag, you could create them as symbols and then add the symbols to the tag. But, they would be a pain because of their limited flexibility. You would have more flexibility for placement if you created a separate flow arrow pipe tag. You can have as many different types of pipe tags as you like. Just switch to the one you would like to have current place your tags and then switch to another type. You can load the multiple tags you created into a project on the Annotate tab > Tag panel > Tag flyout (at the bottom of the panel).
Is it possible to make a flow arrow that knows which way the pipe is flowing? If not, is there a way to use a flip control to control the direction it is pointing? I can't seem to get the flip control option to come up on my ribbon in the family editor when working on a tag. What am I missing?