Floating flooring cannot be 'PINCHED' or anchored into place. It can and will rip itself apart at the seams. I've seen this dozens of times. The fix for THAT issue: have the installer come back (you pay for it because you wanted it run underneath = you chose to void flooring warranty) and cut the floor. They use a floor cutting tool for this. No big deal. Then they use quarter/shoe round to cover up the cut. It is MORE expensive and it gives you the look you DO NOT want. Not good.

Now onto the REAL way to do this. Ideally you install the kitchen cabinets and counters. You get everything shimmed up and nice looking. You leave the kick plates OFF the cabinets (for now...Ikea is brilliant for this very reason). You run the floor UNDERNEATH the cabinets until they hit the feet (leave a little room...use a pool noodle cut into spacer 'O' then cut in half like a 'C' shape and fit it around the legs...pull them off when you finish laying the floor...works like a charm).

Now the floor is installed, pull the foam 'c's off of the legs. Install the appliances and then TRIM the foot plates (the one's that come with the cabinets) and install as usual. No need for shoe/quarter round.

Done. It's almost like Ikea planned it this way (which they did).

If you insist on having the floors laid first you NEED to leave space for the legs to sit ON the subfloor. You can nail 2"x4" onto the subfloor where the feet will sit (roughly) so that you have something rigid to run the floor up against. You leave the wood in place until you get the cabinets delivered. The cabinets are built and put into place and the wood shims are removed on the same day. This option takes a LOT of planning and a LOT of measuring by you and the floor installer. You and the installer will fiddle fart around with the template wood boxes = more money for the flooring install. And you need to be VERY good with your measurements with the appliances. That takes more time and time = MONEY.

Simplest cheapest fastest solution = cabinets first flooring next and then foot kicks last.

We opted to have a thicker toe kick installed to cover the gap as I also dislike shoe mould. I was hesitant to place cabinets with a heavy stone on top of the floating LVP. We plan to install our three small base cabs in the laundry over the LVP with a light Formica top. I think cutting holes for the legs sounds like a huge headache and inviting room for a lot of error. If you don't have a peninsula or island, no one would ever know about the thicker toe kick. Around our peninsula, it just looks like a simple base mould.

@SJ McCarthy That is an absolutely brilliant solution with the pool noodles. Thank you!