Well it looks like you are able to flash your Radeon RX 480 to an RX 580. A user on the TechPowerUp forums successfully flashed his XFX RX 480 with a BIOS from a Sapphire RX 580 Limited Edition. The user obtained the BIOS and then used ATIFlash to complete the process. The XFX RX 480 did have a dual-BIOS and this is something you might want to consider when doing any type of GPU BIOS flashing. After the flashing was complete you can see that the card is now running at 1411 MHz, which is higher than most overclocks that are possible on the RX 480. This is likely due to the increased voltages on the BIOS level.
After flashing was complete the user then ran the card through Witcher 3 and Furmark, which he encountered no problems at all. Flashing your own graphics card BIOS can be tricky and we urge you to do it at your own risk. But it looks like this will give you a nice performance boost to your RX 480.