is there a flammable fluid that leaves no residue?

any fuel that carries some oxgen with burn clean, such as most Alcohol.

But depents on what you are burning it with, and what your detection limits are, very diffcult to burn something else withe Alcohol and not leave any residue.

Only buring the Alcohol all by itself that you may not leave any residue.

If you're planning arson, you will not avoid detection this way. Whether there is residue or not, arson investigators can tell from the fire's pattern whether an accelerant was used.

added later: My apologies. Try ethyl alcohol for your flammable fluid.

Diffrent types of alcohol (not only ethylic) produce a clean combustion, that means there is residue after burning. no smoke either.

You can always use C1-C4 type alcohols and also ethers low carbon ketones(acetone)