If you have a sail loft in your vicinity, you might stop by and buy some scraps, real sail cloth AND double-backed sail seam tape. I've used the stuff and it holds very well for the application you're discussing, if you get it in the .5 to .75 width you wouldn't need to hassle with a sewing machine.

:darts and tucks

I think you might be referring to putting camber in a sail by paneling it together with 2 or more panels. On a small kayak sail, that's not nearly as important as orienting your sail panels so they do not stretch on the bias. You want your sail to hold its shape, that means you need to orient your panels so the stress is NOT on the bias, so you need enough cloth to cut panels that will have the fabric weave perpendicular/parallel to the leach (the diagonal backside to the sail)

You can introduce camber into your sail by cutting your luff (that's the edge that attaches to the mast) with a slight outward curve, say 1.5" over 10 feet. Then, the amount of bend you put into the mast will influence the sail shape. More camber for light air, less camber for heavy air. BTW, the front of the sail is the luff, the bottom is the foot, and the rear diagonal is the leach.