Would jet fuel for an F-16 or F-35 be producible during WW2?
Jet fuel is mostly kerosene, with some aromatic hydrocarbons mixed in for stability, temperature range and the like. You could probably run military jets on pure kerosene if they were magically transported back to WWII, but you wouldn't have to as it would have been possible to make reasonable jet fuel. The Jet-A standard was made in the 50s, and there were no major differences in the fractions available from WWII. 

Before it was an engine fuel kerosene was primarily used for heating and lighting, and it was widely used across the world for that purpose in WWII. It still is in some places around the world where electricity isn't available. The aromatics in jet fuel aren't anything special, so it would have been entirely possible to make a jet fuel. 

You could go farther back than WWII and still run a jet on raw kerosene as the modern process to distill it from petroleum was invented in the 1850s.