I'm using 'intonation' to mean proper well-tempered tuning, e.g., C mid- staff should be precisely an octave (2x the frequency) of middle-C below the staff. On clarinets each note should be in well-tempered tuning with every other; that doesn't happen. As well, there's a 'register key' when opened that is supposed to raise the pitch a perfect 12th - this doesn't work out as it ideally should. A middle-C (right below the staff) goes up to a top-line G when the register key is opened - it should be a perfect 12th but it rarely is. Instrument designers do the best can to make their instruments completely in tune with themselves but it is impossible due to the '12th key'. All the holes that determine pitch (along with the bore dimensions, barrel, bell, mouthpiece, reed and players oral cavity) have an effect on the pitch.
I should add, as well, that the clarinet, within reason, can be tuned to other instruments by pulling out the barrel and/or middle joint. This is routinely necessary as the instrument warms up and thus goes up in pitch.
Intonation in the other sense you're using it, harmonics, are peculiar to the clarinet, as they are primarily odd, not even harmonics of the fundamental.
All of this oddness is due to the fact that the clarinet is basically cylindrical (not conical like a sax or oboe) and closed at one end (where the mouthpiece is) unlike a flute.