We recently had to take up some wood subfloor in our kitchen because it had gotten wet and moldy. We were able to take up the vinyl top floor without damage. It, too, had some wetness and mold on the underside. We have aired it out on a porch and applied bleach, but while the mold is gone, the odor is not.
I agree with the vinegar. It has helped me a great deal. I would also try sprinkling baking soda on top of the vinegar and laying the vinyl out in the sun for an hour or so. You can chemically treat this kind of mold by visiting Lowe's or Home Depot. My husband bought a product for our "windowless" bathroom which had mold on the ceiling and it worked great.
I had to do clean up after water flooded my house and I read that vinegar is great to use. Cheap and cleans and disinfects. The vinegar smell doesn't last long. Leaves a fresh fragrance.