I don't tie 'streamside' but I do keep a small kit in my tackle bag. I'm not fast enough to make them up on the water, can't give up fishing time to tying. I use the kit at lunch or in the evening on a mutli day trip. Can't tell you how many times I found the fish would only take a particular fly and I only had 3 in by fly box.

My travel kit fits in a small PLANO box, it has a small scissors, a small vice made from an exacto blade holder, 3 common thread colors re-wound on sewing machine bobbons to save space, a bobbin bent to accept the the smaller bobbin. An assortment of common hooks, dubbing stored in 1 1/2" sections of soda straws, hackles in grizzly, brown and dun. Some antron in various colors.

Often when tying I end up with small pieces of left over material, these go into a small zip lock and eventually end up in the kit.