Can glucose burn in chlorine?
I have not heard of glucose being burned in chlorine, but I do know that glucose reacts with chlorine in aqueous-buffer medium. See reference 1.
The full paper is behind a paywall. 

It says that oxidation of glucose by bromine water was studied previously and the reaction of glucose and aqueous chlorine also happens in a similar fashion although the reaction is slow and products yield is less. Nonetheless, major product of the reaction is D-gluconic acid in both acidic and alkaline medium but unbuffered chlorine may further react with D-gluconic acid to various products like 5-keto-D-gluconic acid and D-glucaric acid.

Reference


J. Am. Chem. Soc., 1955, 77 (7), 1875–1880. DOI: 10.1021/ja01612a050.