Black spots on my right leg. Its spreading. I have varicose vains. Is this serious?

Maybe. If the dark spots are towards your ankle they may be skin changes associated with venous insufficiency. These can lead to ulcers of the skin over time. Go to miamibeachvein .Com to learn more. Find a doctor at phlebology.Org.
If veins no. Visit your doctor make sure they are veins, spreading black spots are not melanoma serious skin cancer.
Blood in skin. See doctor for evacuation of spots and underlying veins. This can represent bleeding into skin form varicose veins or blood thinning editions. If possible medically, it is indicated to be evaluated as to surgery for the veins. This can often be done with laser as an outpatient office procedure. See a vascular surgeon who performs laser vein ablation.