Proximity to mouthpiece
Obviously, the proximity between my mouth and the mouthpiece is a major factor for both the dynamic of air sounds, and the amount of pitch/resonance the instrument gives back. Many consonants I'd execute away from the mouthpiece, but the interesting states really occur when I'm either directing all of my air into the mouthpiece, or I'm a few centimeters away from it. I'll put up some audio of both, but with blowing a focused air stream straight down the mouthpiece, I can effectively get "pitched air" - the chimera of brass technique that should be impossible. It isn't loud at all, but with mics it could be interesting. This always sounds a half step above the fundamental. I can affect the bandpass of the air with fricative changes, but this is how the resonance of the instrument kind of feeds back.
Direction of air stream
This parameter is much more subtle, and really is only intelligible/useful at low dynamics or low effort levels. So I mentioned how I can blow straight into the mouthpiece - while I'm in this position a little removed from the mouthpiece, I can essentially control where I direct my air. Moving it to either side of the mouthpiece (gradually!) increases or decreases the amount of pitch in the sound without affecting the overall dynamic of the air sound. It would be different if there is a bell-front microphone, since blowing on to the rim will have less air going through the instrument, but that also could be interesting because it's moving sound in and out of the amplified area...
These are standard - any of the sustained fricatives work really well with the instrument. Same with low-to-high filtering of air using vowel formants. Recently, I've figured out a way to get a really present and harsh white noise sound, involving a very compressed "chhhhhhh" mouth shape, in the audio below.
This one I've been rather fond of recently. Since the rolled R (or at least my rolled R) is just fast enough to generate a pitch (around 12-15hz), when using the fluttertongue with only air, I can essentially generate a very quiet subbass tone underneath the delicate airstream. It's something that doesn't get picked up in recordings well, but when I do it in a room, the feeling of the room totally changes due to the slight intrusion of the frequency. Unfortunately I can't hold it for very long (maybe 8" maximum, or 15" if I mainly just roll the tongue with minimal air), but it's a really nice sound regardless. I can speed or slow down the air, altering both dynamics and the friction of the flutter. Again, it's super subtle, so you probably wouldn't perceive it unless this is the only thing that's going on texturally.