Why do my squash plant's get a flower, then a small squash, then tur

http://homeguides.sfgate.com/zucchini-flowers-but-not-produce-26167.html

probably due to a vine borer destroying the vine.

I know what you are talking about. This happens long before the borers get to the vine. My assumption, and I have nothing to back this up, is that if the flower does not get pollinated the plant simply abandons the fruit. You will get other squash, usually more than enough to make up for the few that don't grow.

The fact the the plant already started fruiting means that the environment is good enough for the plant. Take note that to be able to grow the squash bigger, the plant will need to use up a lot of nutrients coming from the whole plant to support the growing fruit. It is possible that there are not enough nutrients supporting the growing fruit. Try applying fertilizer and good enough water. If it doesn't work, you could change the soil where the plant is growing, it could be that there are not enough nutrients in the soil left for the plant. If you suspect pests, try looking for symptoms like worms, puncture holes in the fruit and the stems or any discoloration in the leaves.

Sounds like borers- you got this!! https://www.extension.umn.edu/garden/insects/find/squash-vine-borers/

Your female squash has not been fertilized. The small blossoms are female , large blossoms are male. If the bees don't pollinate your female uterus / squash won't grow. You can take a brush etc and transfer the pollen.

It's a fertilization problem. I've had this happen before. Thankfully, the grow in abundance, so I've always had plenty of squash!

Squash have male and female blossoms on the same vine and it is up to the bees to spread the pollen from 1 bloom to the other to create more squash. If this does not happen, you can help nature along by using a small clean paint brush, like a watercolor brush.