Lots of paens around to the late Milton Friedman, including here from Alex Tabarok who attributes to following to Friedman in Capitalism and Freedom:
President Kennedy said, "Ask not what your country can do for you - ask what you can do for your country."... Neither half of that statement expresses a relation between the citizen and his government that is worthy of the ideals of free men in a free society.
Tabarrok remarks "Damn right."
This seems like a straightforward misreading of Kennedy's statement. He didn't say "ask what you can do for your government" he said "ask what you can do for your country." Surely it doesn't follow from libertarianism -- a doctrine about the appropriate scope of state power -- that it's inappropriate for free men in free societies to act exclusively out of selfish intentions. One assumes, for example, that Friedman regarded his efforts to, say, destroy American public education or make heroin more widely available as things he was doing for his country rather than an extremely roundabout method of personally getting his hands on more heroin.
Closer to the context at hand, it seems exceedingly odd for one of the leading proponents of the volunteer military to object so stridently to patriotic appeals from government leaders -- America's recruits, obviously, get tangible compensation for their military service, but it seems pretty clear that the whole thing would be non-viable without the presence of what you might call a fairly large "patriotism externality" being in play.