Much like the slime fang, dragon fangs are very valuable for their pierce-oriented attack style, but they are usable by different classes, most notably the Harrier and Lancer classes. Dragon fangs are much longer than slime fangs, and are used to make suitable weapons exclusively for these two classes.
For the harrier class, a dragon fang can be used as a makeshift sword, as well as being enhanced by crafting to become a very powerful sword that is excellent for its piercing capabilities. While for the lancer, multiple dragon fangs can be fused together in crafting to make a large spear designed for speed-based strikes and powerful piercing techniques.
Most other classes don't bother with dragon fangs because they are overly pricey, but further uses might be made clear as time goes on in the open beta, as probably the uses for dragon fangs are not only exclusive to the two above classes.