Can I add a kitchen sink drain to a 2 inch bathtub vent. The vent is exactly center to where the kitchen sink drain should be. the 2 inch vent goes through the roof. i know i can wet vent bathroom group.
No.
Kitchens are not part of the bathroom group for wet venting in Washington UPC code.
When a lav drains, it drains through a 1-1/4" tail piece, and pretty slow at that.
A kitchen drains with 1-1/2", and can be a much deeper sink, holding more water.