You can do it any way you want. The tools you have at hand and your skills will help you make that decision.

It can be easy to get a close match with the old and new, however remember that the wood must match in species, grade and sawing.

If you decide to weave in the new with the old, cutting out some of the old planks to slide in the new is how it is done. You can cut some butt seams to preserve more of the existing, but that takes more skill and some tools you may not have. Look at how the floor is put together and select a sacrificial board to cut out so you can gain access to the rest and dismatle the boards...that way you can remove some of them intact to incorporate and reinstall with the new.

Thanks very much for that. I appreciate it.

I've also seen some cool borders, using natural stone or a tumbled tile -- just depends what you have going on in the kitchen and if there is some other material to tie in.