There is a tinderbox respawn on the wrecked ship on the north of Harmony Island.
There is a tinderbox respawn next to furnace in the eastern wilderness ruins.
Searching certain shelves of the Wise Old Man's home gives a tinderbox, possibly book(s) and a message questioning why he keeps so many tinderboxes. This is likely due to Dinoysus's eventual assault upon the Wizards' Tower. Though it is possible to quickly obtain multiple tinderboxes from it, your character will only take one at a time, and only if your inventory has none; this can be easily bypassed through the drop trick.
Bought from any General Store in RuneScape, Dodgy Derek in the Thieves Guild, and from Ignatius Vulcan northeast of Thormac's tower; Searching the Old Mans shelves upstairs and downstairs in Draynor Village; Possible monster drop.