Can spider veins be prevented?

You may be asking whether more spider veins are on the way. That is a fair thing to ask before you spend money on anything.
Can you stop new ones from forming?
my.clevelandclinic.org gives a hopeful answer: "Self-care can often improve blood flow and prevent new spider veins from forming."
The word "often" is doing real work in that sentence. It says self-care helps in many cases, not that it guarantees a result in yours.
What this answer leaves open
The quote is about veins that have not formed yet. Whether the ones you can already see will fade is a different question, and it deserves its own answer from someone who has examined your legs.
Guides that put spider veins in context
For the wider picture, the overview of venous disease puts spider veins in context with other vein problems. The guide to spider veins goes deeper on causes and treatment. If your veins are larger and raised, the page on varicose veins is the better comparison.
The question to bring to a clinic
Before agreeing to a procedure for veins you already have, ask what it changes about the veins you are likely to get next. A good answer covers both.