There is so much wrong with this question (and some of the current answers) that I must address them. I'll do it quickly so I can get on to the meat of this answer. To start with, it's not feedback. To get "classical audio feedback" you need a microphone and a speaker. You only have a speaker. It's not ground loops. In fact, the term "ground loop" should immediately raise red flags about the credibility of any answer. I should write a book about that topic alone. Third, your question doesn't have anything to do with electrical engineering-- only about consumer electronics. Some people here might vote to close this question for that reason (but not me).
The noise you are hearing is from the engine of your car. Want proof? Put your car in neutral (with a foot on the break) and rev the engine. The pitch of the noise will increase with the RPM's of the engine. I am not sure if this noise comes from the alternator or the spark plugs, but it doesn't really matter. The electrical environment of a car is very nasty (and noisy) and this noise that you are hearing is just one of many problems it creates.
The noise is caused by noise on the power/ground of the car. It is easiest to view the problem as having the GND "wire" of the car be at different voltage potentials. When you just have the AUX jack plugged in there is only one connection to GND (through the AUX jack and car stereo) and so it is impossible to have two GND connections. When there is two connections to GND, AUX and your charger, the difference in voltage potentials causes noise on the GND wires to couple into the audio signal.
This is different from having a ground loop because the noise from a ground loop is caused by the current flowing through your charger/phone. If that were the case then the pitch of the noise would not follow the RPMs of your engine.
I should also mention at this point that I have been writing this assuming that the noise is on the ground wire, but it might not be. It is entirely possible that the noise is on the power (+12-ish volts) instead. Many of the proposed solutions apply to either, but keep that in mind.
Solving the problem is difficult, and varies depending on how much you want to mess with your car. The best thing would be to run the charger and the stereo off of the same branch of your car's power system (off of the same fuse)-- and also filter that power with a big inductor (a.k.a. choke) and big capacitors. Unfortunately, this is beyond what most people are willing to do to their car-- and anything less than this is a compromise and will create less than ideal results.
Another solution is to use ferrite beads on the USB cable between your phone and charger. That's what I did for my Samsung Galaxy S2 and it reduced (but did not eliminate) the noise.
You could create a power filter for your charger. This would have a large choke on both the +12v and GND wires, and a large capacitor on the charger side of the chokes. It is important to have the chokes on both +12v and GND because you don't know which side the noise is on.
A fourth solution is simply replace your phone. I know, it's a stupid solution but it could solve the problem. Before my Galaxy S2 I had an iPhone 3gs and it did not have this problem.
A fifth solution is to get a different form of charger. I have an external battery based charger. This thing has a Lithium Ion battery in it and can recharge my phone 5+ times before the external battery has to be recharged. This works because there isn't a second power/ground connection and thus no problem with the noise. Ok, it is still a stupid solution but it works 100% of the time and is better than getting a new phone!
I am hesitant to suggest this next solution, because I haven't tested it. IF the noise is on the GND wire, and the car's fuses are all on the +12v side of things, then it might be possible to simply connect the GND wires between your stereo and your cigarette lighter together. If that new wire connecting the two is short and thick enough then it could equalize the ground voltage potential between those two spots and make the noise go away. Don't do this one unless you are familiar with car wiring and know that this isn't going to mess something else up.
Oh, and the reason why your Bluetooth thing also has noise is the same reason why your phone has noise: It plugs into the cigarette lighter, thus giving your audio system a second power/gnd connector. If you used a different device that ran off of a battery instead of plugging into the car then it wouldn't have the noise. There are several devices like this on the market, but I suspect the the Griffin device works better (except for the noise).