I am no pro, but a few potential issues come to mind:

First, you may want to check with your local government to see if there are rules/restrictions on what percentage of your property can be paved. In my county, it's something like 30% of non-house footprint max.

Second, even if your yard appears to be "well-drained" now, by paving this much area you will be sharply reducing absorption/increasing runoff, even if you leave spaces between the stones. You will need to ensure proper slope and underlayment to the paved areas to avoid puddling/ prevent erosion in those gaps/ keep water from being channeled towards your house foundations.

Third, flagstone reflects sun and gets pretty hot underfoot, and can get slippery if wet. Flagstone with dog-leavings sound even slipperier, and all that rock might be hard on your dogs' legs.

How about combining flagstone patio areas with other more ecofriendly paving? There are perforated paving systems (often used for driveways and the like) which allow percolation and plant growth and would still keep your hounds from digging. Or try deeply-bedded woodchips in some areas, especially under your maple tree?

Lynn

I certainly wouldn't till first as you will only loosen the soil and create a soft bed on which you are bound to get lots of shifting flagstones. Use the compaction you have by skimming off the amount of dirt you need to remove.

However, I would second the concerns voiced about doing the whole yard. Why not do half or a third, and see if it actually performs as you think it will?

I recently had a flagstone patio and wide path put in my yard. It was laid on 1 to 2 inches of sand spread on the existing compacted clay soil. Two big problems came up - the sand between the pavers largely washed away immediately, and earthworms have taken to tunnelling between the pavers, making a big mess. And it's already starting to shift, after only a year. We're going to have to redo it.

If you do go with pavers, they should be set on a bed of 4 inches of compacted gravel, topped with 2 inches of compacted sand. Then sand or a sand/earth mixture (if you want to plant a groundcover) between them. A lot more work, but otherwise you're going to have some problems.

Another issue you may run into is the large, shallow root system of the Maple tree. We had to raise the patio area to go over it.

I second the idea of a perforated paving system. Should discourage digging but would be friendly underfoot. Maybe you could set in a smaller patio near the house, and use one of the paving systems that allow grass to grow through for the rest.

Good luck! :)

Here is a link that might be useful: Turf Pavers

Use crusher fines for level and set of stone, not sand. Mortar outside edge of pad at sharp angle using Portland cement, crusher fines, and sand. Use polymeric sand between joints once your stone level is set, then spray with water.
Soil is precious, please don't leave it under the pad if it is healthy. Use a small machine, strip it, and trade it to a neighbour without dogs for the equivalent volume of road-base (sand and crushed rock) that should be at least 4 inches thick under those flagstones.
Use plate tamper to compact base properly, consider drainage and grade when setting string lines, and maybe plan a shade spot on pad when planning because shadows on flagstone are a beautiful thing in the afternoon sun.
Finally, don't start cutting your flagstone because it is very hard work, and blades are extremely expensive, just have an agreement with supplier that you can return unwanted stones that were included in pallet.

We just landscaped our entire backyard and about 70% of it is in flagstone with two types of thyme planted between the pavers. Our landscaper did not do anythings special with laying the flagstone. We did bring in a lot of fresh dirt and just laid the flagstone down slightly raised above the ground to accomondate the growth of the thyme. We have no problems with the flagstone being slippery but they do get a bit hot in the summer due to the iron in the stone. I would also suggest installing a good drainage system. Van