Kitchen sink and bathroom sink are only separated by a stud wall. Both traps drain into
2"waste line at the same height from both sides and at which point also the 2"vent goes up. So the vent is shared by both fixtures. Is that O.K.

I would see no reason that it would be a problem. Are you have some difficulty? It should be fine. Several drains share the same vent in a house.

Just wanted to know if it is legal

Just wanted to know if it is legal
Yes the two fixtures may share the same vent. Regards, Tom