Can a leg massage reduce the chance of clots forming in my leg veins?

Massage feels good. Leg massage certainly feels great and I encourage you to do it. It does help keep the circulation going. Scientifically speaking I do not know of any evidence saying that it truly lowers risk of clot formation.
Maybe during massage. The scd (sequential compression device) is routine used in hospital patients to prevent clots. This basically massages the legs sequentially! It is effective, but it does the compressions all the time. So I suspect that good massaging of your legs will do same, but only when it is being done. Enjoy your massage, but I would not rely on it preventing clot after getting off the table!