I always carry the ferro rod and some of the stormproof matches. They will light and are great items. The Bic is fine when it works. The bike tube bands are a good idea, they are good for lighting difficlt fires and also keep the Bic from slipping out of your pocket. I have had problems with Bic and other butane lighters over the years. I do carry one occasionally but they can't be relied upon. I have had brand new Bics that would not light and they also break easily.

I normally carry a Zippo, freshly filled with a backup fill from a Zippo keychain tank. A ferro rod, and the stormproof matches. I keep two small containers full of cotton balls saturated with petroleum jelly for instant fire. Never fails. I also always carry a light, fixed blade knife, in case I need to whittle my way into some dry wood.

Your kit will work fine too