The b-c guide to getting jazzy noises out of a clari 
I'm not going to go into improvising or anything like that, I'm going to try to cover three things, some in more depth in others.
1 - High notes. Certainly, if you're going to attempt solos by people like Benny Goodman and Artie Shaw, you're going to want to be confident in notes like 5 leger line Bb/B/C. Plenty of mouthpiece in the mouth is needed, as well as a lot of diaphragm support (no good going half-hearted at these notes). Have a look at several different fingerings (the wfg.woodwind charts are excellent) - some fingerings will work better on some clarinets than others. You need a good reed, too, but not necessarily a hard reed (I play on 3s, and cope fine with these notes).
2 - Vibrato. Two types, both valid, in my opinion. Diaphragm vibrato is achieved by pulsing your diaphragm regularly. Start slowly, and gradually get it quicker and quicker. It takes a lot of work, but you'll get there. The second type is lip/jaw vibrato, and this comes up quite a lot in jazzy pieces (I use it to achieve the 'Stranger on the Shore' effect). This is achieved by controlled wobbling of the jaw/bottom lip, again, start slowly and build it up (it's very easy to make your clarinet sound harsh and unpleasant using this, so be very careful). This is an awful lot easier to demonstrate than describe, if you catch me at an event, do feel free to ask, and I'll have a go at showing you.
3 - Glissandi. Like at the start of Rhapsody in Blue! It's achieved largely through fingers, with a bit of lip/breath control. Play a strong two leger line B. When you're happy, slowly expose the left hand index finger hole to play a C. It'll take practice to make the transision seamless, but you'll get there. The speed needs to be quite slow. Once you're happy there, start at A, slide the middle finger off to play B, and just before the middle finger has left the hole, start sliding the index finger off. You may need to do some lip and diaphragm adjustment (you need tons of support). Then gradually add the other holes, until you get to the D (where I'd start for Rhapsody). You can then use the technique to smear other notes for a nice jazzy effect, and I use this a lot.
Now I bet you're all going to go off to practice all that lot (particularly 3

). Have fun!