Does handling a lot of flour cause fingernails to break?
If this has never happened before and only seems to be an issue with your fingernails (versus excessive dryness in other skin or areas) I'd say it's either:

a. Flour will absorb moisture from your hands if you're spending a lot of time handmixing or kneading. 

b. You're probably washing your hands a lot to remove the flour (and other food particles) and excessive washing with hot water and soap will also dry out your hands.

There are moisturizers that you can purchase specifically to help with your nails. Might not hurt to apply those after you're done with your baking for the day. Also try wearing a thin glove that will allow you to manipulate the dough but keep your hands from being directly in the flour and food. If neither of these things help, you'll want to see a doctor.