The open kitchen design in small residential units where fire load density and occupant load are very high introduces additional fire risk. One big concern is that whether flash-over can occur which may trigger a big post flashover fire, resulting in severe casualties and big property damage. It is important to understand and predict the critical conditions for flashover in this kind of units. Based on a two-layer zone model, the probability of flashover is investigated by a nonlinear dynamical model. The temperature of the smoke layer is taken as the only state variable and the evolution equation is developed in the form of a simplified energy balance equation for the hot smoke layer. Flashover is considered to occur at bifurcation points. Then the influence of the floor dimensions and the radiation feedback coefficient on flashover conditions is examined. When the dimensions of the floor vary, the resulting changes in internal surface area or size of floor area both have effect on the flashover conditions. When the radiation feedback coefficient is of small value, there is no possibility of flashover. With the increase of the radiation feedback coefficient, at first it significantly affects the conditions for flashover and then moderately when it reaches a larger value. It is proved that the flashover phenomenon can be demonstrated well by nonlinear dynamical system and it helps to understand the effect of various control parameters.