First of all; sorry to say but it sounds like you have the diagnosis backwards. If a fuel injected engine like yours dies out when you step on the accelerator; it is NOT "flooding out," it is starving for fuel. When you step on the accelerator in a fuel injected motor; it lets more air in; which leans out the fuel mixture. Backfiring through the intake confirms that it is starved for fuel. This is usually caused by a fuel filter that has clogged up. Please change the fuel filter.
I would also replace the intake air temperature sensor; which is a low priced part that often goes bad and causes the engine to run too lean like this.