I don't know where you read/heard that the Three Rivers flagstone will leach iron, but it isn't an issue in the middle of a garden as a path, and it would be my first choice as the colors really pop, don't waste your time sealing it, just hose it off from time to time. I also wonder if you really need to pay the premium for a tumbled flagstone, the raw Three Rivers flagstone is cheaper and just as nice. In California USDA zone 9 locations, an inch or two of sand is all that is necessary for a leveling base of flagstone used as a stepping stone pathway. If you have clay loam based soil that is too soft, you may have a drainage problem needing correcting, or are just overwatering the area. A clay loam soil is only too soft and subject to compaction after significant rains,(and this is really only an issue for planted areas, where you want to avoid soil compaction when the soil is wet, so you maintain good oxygen exchange and soil texture for plant roots). Even in the middle of winter after heavy rains, a clay soil is fully capable of supporting the weight of flagstone pavers without problems of movement, but the sand base will help make them more stable. Weed fabric below a base material is really only appropriate/necessary when you are wanting a solid area of flagstone paving and want to reduce weed growth at the joints; when laying out more widely spaced flagstone as a path, I'd think you would want some low ground cover between the flagstones. If you don't, then use the weed fabric and mulch with gravel or decomposed granite between flagstone pavers. If you are trying to lay flagstone stepping stones on a slope, there is considerably more attention to a stable base necessary, and I'd suggest you get professional help to install it for better results. I'd also suggest you go to your local library or buy one of the Sunset or Ortho gardening books that address landscaping and dry laid flagstone paving, they both cover all the issues you will likely face in your installation, and are generally a more reliable source of information than asking questions on the internet. If you are really interested in the best methods for installing a lower water use garden using California natives, you should also do some reading up on issues of soil drainage, best time of year for planting, how and when to water, importance of mulching, etc., as there are better ways to do this to save time, money and water.

If you are using flats of groundcover or even purchasing them in individual plugs or pots, there is sufficient soil already attached to the roots to get them established. One characteristic many groundcovers share is a very shallow and spreading root system - they don't need much soil to keep them happy. I have quite the assortment of various groundcovers growing in several inches of crushed rock under my GC tables at the nursery - little chunks broken or dislodged from the larger containers - and they thrive in virtually no soil at all! I'd fill between the pavers with the sand and plant the plugs of groundcovers as is, with the container soil attached to the roots. As long as drainage between the pavers is good (and no reason it shouldn't be), they get enough sun, you don't walk on it too frequently for a couple of weeks and water as necessary, you should be good to go. No need to fertilize - most GC's require none. This is the method I've used both professionally and at my home. I've got a variety of different groundcovers growing between recycled concrete pavers set in a crushed rock base - no added soil except what was attached as they came from the pots.

The flagstone walk I built four years ago has many pieces that are 3"x4" or even smaller. They have not flipped or shifted at all. HOWEVER, I did use polymeric sand in between the stones, so that helps keep them in place. What are you going to use between yours, to plant the thyme in? I agree with Patty Cakes that weeds would do as well as if not better than the thyme, unless you plant a lot of thyme immediately. Even so, it could be a maintenance nightmare. How much to you like weeding?

'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...