Quoting from Zed on discord:

My suggestion would be to make a tag for the flint axe and use the tag in the crafting recipies [sic]. This would allow players/pack makers to more easily add other axes as possible tools for the recipe. You could also add the vanilla axes to the tag, or not depending on how you feel about that. Just including the flint axe leaves everything how it is, but makes it easier to adjust. Currently, to have another axe, each recipe needs to be added for every type of wood, including each stripped log if desired. Adding it to a tag would be easier.

If the sticks and planks recipes used an axe tag instead of the flint axe specifically, that would help pack makers add other axes as they see appropriate.