The TSA Prohibited Items web site should give you most of the answers.
Virtually every fuel is prohibited, but there are some exceptions. Most standard fuels are prohibited, and that includes liquid fuels (e.g. white gas and alcohol), gaseous fuels (e.g. butane), and solid fuels (e.g. Esbit).
There are many exceptions, such as drinking alcohol. If you inquire to TSA, they will refer you off to DOT where they can look at the MSDS on any substance and tell you about the flammability.
Theoretically, they can prohibit a simple wax birthday candle. However, in practice, they probably would not unless you had a suspicious quantity. Theoretically, wood is a fuel. Of course they make airline cargo pallets out of wood. That is a typical gray area for the regs.