This gets a bit tricky. Lots of great groundcovers for heavy shade, but few that remain very flat and low growing and suitable for planting between flagstones. Two that come to mind are Corsican mint (Mentha requenii) and baby tears (Soleirolia soleirolii). Both require evenly moist conditions and are a bit tempermental. They may not be fully evergreen in your climate (baby tears acts semi-herbaceous in my zone 8, pretty much disappearing in winter and returning well in spring). You might find it easier just to allow a woodland moss (not Scotch or Irish - these are not true mosses and require more sun) to fill in and grow. Or fill between the pavers with crushed shells, gravel or even decorative ground landscape glass.

I was thinking of moss too. I have lots of it around the yard, and I scrape some off and stick it in between the field stones I use to make pathways. I think it looks kind of nice. Just be careful if you are walking in the rain!

Dee