An Ellingham diagram is a plot of the standard Gibbs free energy of formation ($\Delta_f G^\circ$) of oxides as a function of temperature. Let's analyze each statement:
(A) It provides an idea about the reduction of a metal oxide. This is TRUE. By comparing the $\Delta G^\circ$ lines for a metal oxide and a reducing agent (like C or CO), we can determine the temperature at which the reduction is thermodynamically feasible. A reducing agent can reduce an oxide if its formation line is below the metal oxide's line at that temperature.
(B) It provides an idea about the reaction rate. This is FALSE. The Ellingham diagram is based on thermodynamics ($\Delta G^\circ$), which only indicates the feasibility or spontaneity of a reaction. It provides no information about the kinetics or the rate at which the reaction will proceed.
(C) It provides an idea about free energy change. This is TRUE. The vertical axis of the diagram directly represents the standard Gibbs free energy change for the formation of one mole of the oxide.
(D) It provides an idea about changes in phases. This is TRUE. The slope of each line is related to the entropy change ($-\Delta S^\circ$) of the reaction. There are abrupt changes in the slope at temperatures where a reactant or product undergoes a phase change (melts or boils), because the entropy of the substance changes significantly.
Therefore, the incorrect statement is (B).