Go the extra mile; site and mark your diameter, break-up the flagstone within the circle and remove it. Now you can rough level the ground and install steel edging. Builder's sand (aka C-33) goes down and a plate compactor is used. The most difficult, time consuming, and important part is achieving a level surface, a length of heavy (non-flexible) pipe will work.

Thanks for the reply. Yes if removing the patio was an option then I wouldn't have the dilemma, I would then have a standard install situation with lots of good DIY videos to follow. BUT better half has declared that patio should stay in case we ever change our minds, tire of the pool or decide to move. The patio is not flagstone but built of old original river rocks like 6" deep and 12" long, not an easy demo even if I was permitted to...thus still trying to figure out how to do this without digging. Thanks again for the reply!

Do you have plans to set up any type of filtration to this? If so, any pumps or any electrical devices connected to it, must abide by the National Electrical Code requirements. Particularly, bonding of the vessel and it's perimeter.

Also, VGB compliance for suction inlets.

IMO sand is not a good idea for any kind of need for level since it shifts constantly . What you need is exactly what every other hot tub needs a good concrete base.

Well, because you want to preserve the patio underneath, here's a couple ideas (not tested and true, just ideas). Idea #1: use landscaping block to build a circle slightly bigger than the tank, thus containing a layer of sand 2 to 3 inches deep (which should be enough to provide a smooth top layer, unless your patio is a lot bumpier than it looks). There are many blocks styles and colors to choose from. You'd probably need to mortar the first layer onto the patio, but that wouldn't be too awful to remove someday. It could possibly look like a decorative ring of steps around it. Idea#2: use exterior grade plywood to build a circle the same size as your tank. Use old carpet padding underneath, to even out the bumps. Or, use a lot more of the beams.

Come to think of it, I like idea #1 better than #2.

Agree with idea #1, mortaring the wall blocks to the existing stone and to each other. The addition of a vinyl pool liner would block any voids. Rental of a small lawn roller for sand compaction.

Make a steel ring with landscape edging, fill with a crushed stone-dust mix, level it, compact it, and install the tank.

https://www.lowes.com/pd/COL-MET-Brown-Powder-Coat-Steel-Landscape-Edging-Section/3015401

The better half is right to not want to demo the patio. :)

I've put that foam insulation board under smaller tanks (but approximately the same PSI) to even out bumps. It holds up well...indoors...