All of the wooden variant chests from Quark are able to catch fire and burn. I did not find anything mentioning this as a feature of the variant chests, and I did not find anything in the config file when searching with relevant terms. Nether Brick Chests do not catch fire or burn. Vanilla chests and chests from other mods (when they're installed) do not catch fire or burn.

The following log and images were tested with only Quark and ARL installed.

https://pastebin.com/siftQM8s