In this case I'd say the face of the jamb goes the non-kitchen color.
Usually the doorway jambs go the color of the main part of the house.
Someone mentioned a good rule of thumb -- go with the more neutral [or
lighter] color on the jambs.

It's personal choice, of course.... for a dining or some other room
that's set off by doorways, some people like to have the color of the
set-off room "leak" out into the main part of the house. This is the
opposite of what I would call the normal way.

You could try to visualize -- stand in each room, away from the door
way, and imagine seeing the other room's color "leaking" out.


Right, you can either try to hide the transition, or decorate it.
The simplest solution is to add trim, in a color contrasting
to both rooms. Failing that, paint a border, or interleave
the two in a complex line of division.