From the Airventure site:
Fire Safety
The Oshkosh Fire Department strictly prohibits wood campfires and charcoal grills (per National Fire Protection Association standards) anywhere in the aircraft camping areas.
Use of white gas or propane-fired camp stoves is allowed in aircraft camping, provided they are used in an area well away from parked aircraft and that the stove is attended at all times. It is strongly recommended that aircraft near the stove be checked for any fuel fumes or leakage, and the stove be elevated above ground level.
In practice nobody cares much about cooking apparatus, smoking, or alcohol consumption inside individual campsites despite the general prohibitions as long as you keep reasonably to yourself.