It all depends on how much smoke the stove emits during the cooking process. I've seen some kerosine stove that work almost completely like gas stove with very little smoke emissions. If the opposite was the case, then the risk of landing a respiratory complication is highly possible.
Exposure to smoke in general, especially from burning flames can pose a major health threat to our body by attacking the lungs and other organs primarily responsible for respiration. This is because smoke produce and released by any most of burning fire is usually a mixture of particles and chemicals produced by incomplete burning of carbon containing materials. And as we know, we breath in oxygen which our body is need of to pump air into our system. We then expel carbon dioxide which is in the form of bad air our body rejects. Taking in carbon base air from smokes is a complete reversal of what our body needs. Hence, If we are to put this explanation into consideration, then smoke released by a stove can pose some serious respiratory issues, given that the stove works on kerosine which contains more corrosive elements.
However, as I said above, it depends on the amount and consistency of smoke inhaled. Almost everybody can have a respiratory shut down if they were expose huge amounts of smoke. An instance will be someone stuck in a burning house. In other cases with very little smoke exposure like from a kerosine cooking stove, I'd say It depends on our different body strength. Some people can work around stoves all their lives without having to develop any respiratory issues, while others can't because their body system isn't strong enough to handle it.