Options for skirting board on slightly different levels
There are a few different options that I'd consider:


Ordering made-to-measure skirting for the dining room that's taller than the skirting you have the kitchen, but with the same top profile. This allows the tops of all skirting (and hence the grooves) to line up.
Stepping it down with a transition piece. You can either cut at 45 degrees and have the transition piece run vertically, or cut at 22.5 degrees and have the transition piece run at 45 degrees. In the following diagrams the black diagonal lines represent cuts, while the blue lines represent one of the grooves on your skirting. Note that the 45 degree transition in version A leaves a gap underneath it, which will require wood filler before painting. Or alternatively the transition can be moved to the right to avoid this, version B, but this leaves the skirting looking too low at the end of the kitchen.