Simple answer: No, that will not work as a flak vest.
Almost every single paintball vest out there will not pass muster unless you're doing legacy style plates that cover the whole thing.
A more practical solution would be to make one yourself from a thick fabric like pleather, leather, or duck cloth. You can usually find a good, thick fabric for under $15 a yard. I'd recommend going to smaller, non-chain fabric stores to find those really good deals.
Or you can buy one from someone. A Jango style vest is going to cost you at least $50 from pretty much any vendor.
If you want to save money, make your own vest. If you don't know how to sew, there was never a better time to learn!