Can a solid fuel burning appliance be connected to a chimney flue that serves a fuel oil-fired appliance?
For new installations, it is prohibited unless your appliance is listed for such an install. An example might be a hybrid Wood/Oil furnace where there are safety interlocks between the two systems. Also, there may be a grandfathering clause in your locality. For example, In Maine:
Sec. 1. 25 MRSA §2465, sub-§1-A, "may not prohibit the continued use of an existing connection of a solid fuel burning appliance to a chimney flue to which another appliance burning oil or solid fuel is connected for any chimney existing and in use prior to February 2, 1998 as long as sufficient draft is available for each appliance, the chimney is lined and structurally intact and a carbon monoxide detector is installed in the building near a bedroom. "
Best bet is to call your local fuel board.