I don't necessarily have a "kit" but I carry/have some of the following items on my person, in my pack and in my bike bags regularly:
I always have a knife, light and lighter on my person...always. (Small Gerber, Maglite Solitaire, Bic lighter in a cordura sheath I made, about the size of credit card wallet)
-Tapioca straw sealed and filled with Petroleum Jelly Cotton balls. (Make them up any length you wish)
-K&M Brass Matchcase with Stormproof matches
http://www.kmmatchcase.com/-Gobspark Armageddon Firesteel and scraper
http://firesteel.com/gobspark-armageddon-firesteel/-"Tinder Tube" they can be made from a variety of materials and designed differently. A couple of examples:http://www.youtube.com/watch?v=ZsI6H0zx0BA and
-Orion Signal/Fire Starter especially handy for Winter months:
-Wetfire, Trioxane, Weber Firestarter blocks, all work relatively the same.
-Char cloth, candles (the white Menorah candles are small and affordable) "Magic Re-lighting" birthday candles are another option.
-Fire ribbon/paste (nice for priming SVEA123 stoves)
-Small vial/container of Coleman's camp fuel, Oil Lamp fuel or similar. HEET can be used but be careful about getting it on skin (methanol poisoning IS a possibility)
-Fatwood
-Small folded piece of aluminum foil is nice to have and takes up little space as well.
Any combination of the above will do the job, I like to pick a compilation that provides quick fire, sustained lighting ability (wind, snow, moisture situations) and ability to be easily re-ignited. Remembering that "one is none, two is one" mantra works. Have some on your person as well as your bags so if by chance you are separated from your other gear, you still have a few of the basics. Just some ideas to throw out there, others may have something that works better for you....