Are frequent nose bleeds a sign of leukemic cancer?

Usually not. Most nose bleeds occur from a network of blood vessels near the tip of the nose, little's area. Most of the time it is due to rupture of one the vessels in the network due to dryness, minor trauma or inflammation. Leukemia can cause nose bleed, but that would not be high on my list if an otherwise health person has nose bleed.
Can be but many ... There are many reasons for frequent nose bleeds and leukemia is one of those reasons. But there are many much more common etiologies. You should see your primary doctor or an ENT specialist to have this evaluated.