I fitted a built-in washer recently, from memory the space either side is a lot smaller than 15mm, more like 5mm at best.
If you can move one unit along to make the gap correct when you fit your built-in one you’ll be ok. You need to make sure you can fit a standard door to the front of the appliance, this will determine the gap you leave.
Space at the top under the worktop not an issue, as in the case of my washer, there is about 40mm gap.
Hope this makes sense.