The dark spots on my outer thighs look and feel like veins that reached the surface, so-to-speak. How can I get rid of them?

Thrombophlebitis. This is likely a superficial vein that has gotten inflamed an clotted. Try NSAID for a few days and warm compress. If not resolving get checked.
See vein specialist. If you have veins forming then you should see a vein specialist for a full venous evaluation including a venous reflux ultrasound. Depending on the types of veins that you may have and the results of a venous reflux ultrasound, there are many alternative to treatment .