The dust in itself should not burst into flames spontaneously under normal circumstances. However, fire is a real thing when you’re using a cnc on wood. Winston Moy has a video on the subject that’s definitely worth watching: I Almost Set My CNC on Fire - Let's Talk Shop Safety - YouTube
Personally I’m also using some dust collection to keep the work-area clean while milling and I’m really happy with this. It has been discussed in other topics as well: CNC vacuum (too much wood dust) - #8 by brvdboss
I have it connected to an old home vacuum in the lowest setting and with a cyclone dust collector in between and I must say I’m very pleased with the result.