Buy a stronger power supply unit then. Alternatively, use an amplified speaker and plug it to the jack on the head unit of the TS-480. Plugging it there will disable the built-in speaker of the head unit and the flashing of the display will stop.
Have a look at the power supply unit and see how many amps it is good for. If I recall correctly the one for Control-RRC should be rated for at least 1 Amp (but I may be wrong). I bought one on eBay, very inexpensive, that is rated for I think 5 Amp and I power other stuff with it, too. No more flickering... :-)
Marvin VE3VEE