Xbox 360 error 3 flashing red lights is an error that usually occurs when the console or its power supply has a hardware problem.
1. Let Xbox 360 cool down
Xbox 360 error 3 flashing red lights appears when your Xbox 360 and its adaptor is overheating. Let it cool off. Then make sure the Xbox 360 ventilations are not covered by dust or anything that may block the air from passing. Also, make sure the adaptor is not covered.
Note: If the heat is not the issue see solutions below.
If the flashing red lights reappear again due to overheating, your Xbox 360 might have a problem with its cooling system. If this is the case warranty the console. The thermal paste might be the caused or the heat-sink may have lost its contact with the GPU and CPU chip causing the heat problem.
If the warranty is already null, open your Xbox 360 and replace the thermal paste. Make sure the heat-sink is properly placed to have a contact with the chips.
2. Remove all peripherals
"Xbox 360 error 3 flashing red lights" appears also when the console diagnose a defective peripheral is connected. It could be the hard disk drive, USB storage device, the display cable or the adaptor.
Try to, remove all peripheral that is connected to the console including the hard disk drive except the adaptor. Power on the console, if the flashing red lights disappear, one of the peripheral is defective. Try to reconnect the peripherals one by one to determine the caused.
If all peripherals were removed, but still the 3 flashing red lights still occur, it is possible a hardware inside is damage defective. Warranty your Xbox 360 so that it could be repaired. If the warranty is already void, check this solution here.