Q.Are red berries on dogwood trees next year’s flowers
Squirrels are eating the red berries on my dogwood trees. Are they eating next year’s flowers? Also, I purchased two dogwood trees two years ago and they have never bloomed.

No, the red berries are the trees' fruit, formed after the flowers were pollinated. The buds form on new growth in the spring. Since your trees are only 2 years old, that is probably why they haven't flowered yet; many plants need to have a few years on them in order to perform reliably. However, here are a couple of articles that you may find useful: https://www.gardeningknowhow.com/ornamental/trees/dogwood/dogwood-tree-not-flowering.htm
https://www.gardeningknowhow.com/ornamental/trees/dogwood/caring-dogwood-trees.htm