I would stay away from fatty items such as salmon and prime rib steaks, they let off a high degree of fat and could, idk, could start a fire down the road
I'm not sure where having a fire from this grease within your stove or flue is a problem. The amount of grease that would remain unburnt and allowed to build up, rather than exit with the smoke, could only be a small fraction of the creosote that builds up with even normal stove use. A flue that sees daily temps up to 1000f is a lot different than a range hood and exhaust system. For cooking the occasional (or even daily) steak at home, I can't see anyway the risk of a problem would be significantly greater than zero.