In of itself, one Factor V Leiden mutation increases your risk of getting a DVT (without a vein procedure) 7 times compared to a patient without a heterozygous mutation (one gene). If you inherited a gene from each parent - also known as a homozygous state - you are 80 times more likely to get a DVT. Either way, we treat a lot of patients who may have Factor V that we don't routinely check for - the incidence of DVT after sclerotherapy is low. We only check for mutations in patients who have had a DVT spontaneously - no obvious reason why they got a DVT.
It looks from the picture that you need foam sclerotherapy in the lower leg. Consult a board certified vein specialist - credentials from the American Board of Venous and Lymphatic Medicine (previously called Phlebology). Read about DVT and watch videos about sclerotherapy on the link below.
Even with a factor V Leiden deficiency, the veins that you show can be treated safely. You seem to have a combination of spider and blue reticular veins and the lower calf veins may be varicosities. It is hard to tell from the photo. You should see a vein specialist for a full venous evaluation including a venous reflux ultrasound.