Please recommend a Flash for OMD

Yes but not really. The puproar of increasing shutter speed is to decrease the ratio of ambient to flash Lighting. This works because the flash puts out all of its light in say 1/1000th of a second. In a pitch black room you would get the exact same exposure with a flash at full power whether the shutter speed was 1/10 or 1/250. Now add ambient light. With the flash off, you get a brighter exposure at 1/160 than 1/250. Basically you use shutter to dial the ambient light up or down. Then you balance the flash by adjusting the power level. LEDs however are effectively just another kind of ambient light. The only way for an LED panel to match the ambient light is to be brighter and that takes a lot of power if we're talking about sunlight.