We painted the kitchen. The master bedroom door faces into the kitchen. Should the side of the door that is in the kitchen be painted the same color as the kitchen?
Typically a door has the same color as the frame and trim around it. But, don't feel that you have to be constrained by tradition. By painting the door the same color as the walls it will be blended with the wall. You will still have the door frame to deal with. The frame can also be the same color as the wall or it can be an outline with a different color.
The door can also be accented with a complimentary color that goes well with your kitchen. This accent color can be pulled out of the cabinetry, flooring or window coverings. This can be a very bold or subtle look. It comes down to what you like.