How can I blend my dining room with my kitchen that is white and gray?

As a retired interior decorator, I would always tell my clients that one color from each room should appear in the next room to maintain continuity and flow. If your kitchen is white and gray, just use one of these colors in the DR and introduce another color in the DR.

Say, for example, that your DR and LR connect, and your LR is done in blues and yellow. Do the DR in blue and gray, or yellow and gray. Then as you walk from the DR into the kitchen, the gray carries in there, but the yellow or blue drops off and white picks up.

I do want to add that it really takes THREE colors to make a color scheme. If you look through shelter (decorating) magazines, you will see 3 colors in each room, even if the 3rd color is just a green plant or a vase of pink roses, etc.

You could switch the colors. If your kitchen walls are white paint your dining room walls grey and the trim white.

I would try to bring in some whites and grays into the dining room. Either paint the walls a similar color of the kitchen, maybe a different shade. You could bring in some accents that are gray or white to tie into the kitchen too such as place mats or table runners.