We put in a flagstone path a few years ago and it's holding up great. However... our ground is basically pure sand under the top soil, so drainage is not an issue for us. We removed the sod and made a trench about 6" deep. We added about 4" of diamond dust (crushed limestone) and then set the stones on top. Our stones were not very uniform in thickness, so it took a long time to get them level and so that they didn't rock when you step on them. Then we packed more diamond dust between all the stones. We have had no frost heaving or settling at all, and I think only one stone has cracked. This is on the north side of our house and the moss filled in all the spaces on it's own. We do get a few weeds and those little Johnny Jump-ups like to spring up between the stones, but I just use a little round-up on the weeds maybe once or twice a year.

I would check with some gardeners in your zone to see if your plan is feasible; in your zone I am wondering. It is not clear from your post what your soil type is, or how much rainfall you get. Before digging holes between 2" thick flagstones , I would want to know if there were any locally available plants that could survive in those conditions. You don't just have DG between your flagstones, but as an underlayment as well. How thick is that, and are the flagstones far enough apart to actually dig holes? You could easily green up the patio with a few potted plants that favor your zone 10 conditions, perhaps flanking a nice fountain, and edge or juxtapose the patio with herbs or other plants of your choice with flagstones between them. That would allow you to test a number of plants in your zone to see how they would respond to those conditions. I am in zone 6b, so hopefully others in your zone can be more helpful. It sounds like you have a nice patio right now, and I am assuming you expect to place plants that will last and look good for a long time. The specific plants you select would dictate how large and deep the planting holes would have to be, and what soil type would need to be added.

This may not be to your taste, but there's a native perennial lippia (Phyla nodiflora) that does very well between stepping stones. I've never seen it available for sale, but you may already have it as a lawn weed, or if you keep an eye out for it during its blooming season, you might easily spot it between the cracks of a sidewalk near you. I found some among the weeds along an asphalt bike path a few blocks from our home and transplanted it into our yard last spring. It does (obviously) have weedy tendencies (I now have two patches of it across the yard from where I planted it, in addition to to the patch that I actually planted), but so do purple alyssum and really most plants that do well between stepping stones. If it shows up somewhere you don't want it, it's easy to pull. Most importantly, to my mind, it's quite pretty, remains in bloom for about six months (May through October), stays absolutely flat to the ground, and seems perfectly happy to bake in dry, cracked clay all summer but sit underwater for weeks in the winter. I'm expecting mine to die back to its roots for a short time in winter (though it's shown no sign of doing so yet) - but in places with milder winters, such as the Bay Area, it's evergreen. Here is a link that might be useful: CalPhotos: Phyla nodiflora

'Georgia Blue' Veronica ped... is lovely in all seasons of the year here & for me grows about 8" tall flopping a bit. It doesn't like to dry out, but it does like good drainage, so not sure if it would work for your area. Thymes are excellent, but need to be carefully weeded until established into a carpet. Takes precision fingers to do it, but it can be done. The dense top holds a bit of moisture & I find weeds germinating right inside it, but they're easy to pull. The bird seed might be the source of those weeds...