High power LED lamps for use in lighting products, such as flashlights and the like, are formed of a plurality of LED die arranged in a multi-dimensional array, each of the LED die having a gallium nitride semiconductor layer and phosphor material for creation of white light. Each of the LED die emits light from the top, bottom and sides of the die and is arranged on the multi-dimensional array so that the emitted light from each of the die does not contact another die. A reflector gathers and focuses the light from each of the die to approximate a high power LED lamp. A thermally conducting, electrically insulating material or phase change material is incorporated into the lamp to act as a source of heat removal.