Bottom line -- if you have flaps, you can slip. Just know what the effects may be. You can read about it in the POH. You won't find a "prohibition," however.
Every Cessna 172 factory owners manual from 1956 through 1971 said this (this is copied form the manual for the '66 C-172G):
Yes, I know the current TCDS only says "avoid", and the old owner's manuals don't carry the force of law ... but when people say they were told slips with full flaps were "prohibited," they're not making it up out of whole cloth.
What did Cessna's Manager of Flight Test and Aerodynamics say about this issue?
With the advent of the large slotted flaps in the C-170, C-180, and C-172 we encountered a nose down pitch in forward slips with the wing flaps deflected. In some cases it was severe enough to lift the pilot against his seat belt if he was slow in checking the motion. For this reason a caution note was placed in most of the owner’s manuals under “Landings” reading “Slips should be avoided with flap settings greater than 30 deg. due to a downward pitch encountered under certain combinations of airspeed, side-slip angle, and center of gravity loadings”. Since wing-low drift correction in crosswind landings is normally performed with a minimum flap setting (for better rudder control) this limitation did not apply to that maneuver. The cause of the pitching motion is the transition of a strong wing downwash over the tail in straight flight to a lessened downwash angle over part of the horizontal tail caused by the influence of a relative “upwash increment” from the upturned aileron in slipping flight. Although not stated in the owner’s manuals, we privately encouraged flight instructors to explore these effects at high altitude, and to pass on the information to their students. This phenomenon was elusive and sometimes hard to duplicate, but it was thought that a pilot should be aware of its existence and know how to counteract it if it occurs close to the ground.
(Cessna — Wings for The World, by William D. Thompson, Maverick Press, 1991, p. 41, emphasis added)
You'll notice that beginning with the 1972 model year ('73 for European-built models) 172s have a larger dorsal fin. This apparently eliminated the "pitch-down" problem, and the word "prohibited" was replaced by "avoid" in the owners manuals.
However, there is also an unrelated, more benign phenomenon that Thompson described in newer models in full-flap slips: “a mild pitch ‘pumping’ motion resulting from flap outboard-end vortex impingement on the horizontal tail at some combinations of side-slip angle, power, and airspeed.” This really isn't a problem and it's not limited to Cessnas -- my Sport Cub does it, as well.
So although the 172L’s larger dorsal apparently solved the pitch-down issue, they kept the cautionary note in the POH because of the latter phenomenon.
Unfortunately Cessna contributed to the “end of the world” fear of slips with flaps, by not explaining the pitch-down phenomenon in the manuals.
It really does work quite well, doesn't it?
