What is the fastest BPM a horn can play chromatic scales? Is a chromatic scale of 16th notes at about 150 BPM too fast?

I can't tell you the fastest, there's always someone faster. What matters is embouchure, tongue speed (if we're talking staccato), valve throw, and valve alignment. I have an older German horn that has very fast, short throw valves. I can move much faster on that than my Paxman which has a huge throw. My single has a long throw but probably the best valves I've ever seen and they return amazingly quickly. Holtons, at least all that I've played, have pretty fast valves.

I was talking legato. 16th note legato chromatic scale at about 150 bpm. That's not too fast?

I tested out on my 4 horns, a 60's and 80's Paxman, a geyer single, and a Dressel compensator. 16th at 150 slurred can be done on the faster horns (60's paxman and Dressel) and kept going for awhile but they got a bit sloppy as not enough time to get a really solid breath. The 80's paxman (a 25A) with longer throw valves just was not feasible for long at all. The Geyer single is extremely nimble and was pretty darned easy to do this on, and being very light (ridiculously so) didn't tire on it, but in the high register of course pitch and accuracy became an issue. Hope this helps.