I've been machining titanium for a few years on a hobby lathe, then heat-treating it to bright blue with a butane torch, and it never occurred to me there was a fire risk. So far as I know, none of my workpieces or swarf was ever near to catching fire.
The stuff is tough, and I think that's why the swarf parts relucantly and with a fair amount of heat from its parent stock. But with a sharp HSS tool and a lowish speed, you can dig deep and peel away lots. Most of what I do with it is decorative rather than functional, and I'm quite happy to use HSS – carbide doesn't seem justified.
Blue items are titanium, the others PB102; all done on a Warco WM250V and a Sig C0. No coolant apart from the odd squirt of WD40:-
