My apologies if this has been covered, which I'm sure it has - but I searched a lot for "toe kick saw" and the search function stated "No posts were found because the word saw is not contained in any post."

Please delete this if necessary and there's already a post for it!

I'm doing engineered click over plywood subfloor.

The kitchen's cabinets were installed over the previous oak hardwood in place.

I've seen a lot of good info on using a toe kick saw up against the toe kick to remove the "exposed" flooring not under cabinets, then installing new wood up against the old.

To visualize, my kitchen cabinets run around 3 walls of the room.

My main question is around the expansion gap - do I put the expansion gap against the single non-cabinet covered wall? Or do I just leave an expansion gap against the old flooring under the cabinets, and install some rounded trim in the toe kick to cover the gap? The latter option doesn't seem to make much sense.

Thanks for your input!

You may be able to remove the toe kick boards before you run the toe kick saw along the edge of the cabinets, then re-install them after the new floor is installed.
Depending on the thickness, you could have a little bit of expansion gap there. I would rather install new, thicker toe kick boards instead of adding shoe molding, but shoe molding will give you the expansion space and would conform to the floor easier than a solid wood toe kick board. Shoe molding is easier to install than quarter round and the nails go into the wall, or cabinet without angling into the floor, which would defeat the expansion space.
You may want to have an extra blade for the saw, since there will be nails from the old flooring that you could saw through without seeing them.
Shoe molding would cover an expansion gap next to the old base board at the wall so you would not need to remove the base board.

Thanks a lot! That helps. I think the toe kicks are fixed to the cabinets, but I'll see what I can do there because that would solve the whole problem.

If I can't do that I will have to figure out shoe molding - only big issue will be matching it to the cabinets, we're going with much darker floors.

One dumb question - an expansion gap needs to be in place on every side of the floor, not just one, correct?

Once again, greatly appreciate your tips!

You will never need expansion gap at the ends of the boards with oak flooring. It won't expand lengthwise much, ever. It is a good practice to have gaps at each edge of the room, if possible. If the floor gets flooded there will be a lot of pressure from the flooring expanding against the walls before the floor starts to buckle and come loose from the sub-floor. Tons of pressure can be developed, enough to push walls.This is a worst case scenario, but can happen, so take care.
Since we don't usually do any painting or have wood other than the flooring I will use the same material for the shoe molding as the new flooring. It doesn't look bad.