The only vent needed is at the sani-tee where the sink trap connects. No vent is needed on the line in the slab. The purpose of the vent is to protect the trap seal.
If you do run 3" under the slab a full size 3" cleanout is required.
A 2" line is sufficient for a kitchen sink.
2" is a minimum pipe size underground.
The sink should connect to the main on a horizontal plane using a Wye and 45 or, a combo.