Pictures are a must post her ein a comment do not use screen shots just jpeg

Look for groundcover between the flagstone for your growing zone at a local nursery, not a big box store. Once they become established, they will help keep weeds down.

I don't know of any yard that does not need weeding.

pea gravel or hardscape stones can be purchase at most garden centers, ACE hardware, or Big Box stores.

Unfortunately, weeds will germinate in the pea gravel, as well. I have had them come up in pea gravel when underlayed with a double layer of landscape cloth. It will slow them down a bit, though.

If you are not wedded to the flagstones, I would remove them and use a different walkway material -- square concrete pavers -- they could even be laid in an interesting pattern. It would help if you could put a photo of the area! You are walking on this area with bare feet at least at times, and an uninterrupted level surface would be more comfortable. I've laid paths with the concrete pavers from Home Depot (very inexpensive -- they used to be $1.50 per sq ft) on a weedcloth and pea gravel bed and they have held up well to light foot traffic. Pavers that butt up against each other do not need sand or anything in between them to hold them tightly together, as long as you have tight edging.