The voltage-current characteristics (VCC) of flame-assisted electrical coronas have been measured in an inhomogeneous electric field. The electric field was created by applying a voltage less than 25 kV DC between a cylindrical metallic burner and a planar metallic grid, which was perpendicular to the axis of the burner. Both positive and negative polarities of the applied voltage were studied in the presence of a pre-mixed methane-air flame. The results were compared with the VCC measured for the same discharge gap in the absence of a flame. Simultaneously, with measuring a VCC the behavior of the flame was observed and its height was measured under a gradually increased voltage, which resulted in the flame shortening. For most cases complete extinction of the flame was achieved at a particular voltage. An exact spherically symmetric solution for a unipolar corona in the domain between two spherical electrodes, was used to model the discharge gap between the flame boundary and the grid and also to calculate the VCC for comparison with the experimental results. It is shown that in the presence of a flame, the experimental and theoretical VCCs can be matched if the radius of curvature of the flame tip increases with the total current. This agrees with the present experimental results, in which flattening of a flame was observed when the current was increased.