Putting a bunch of amps on one output should be no problem at all, but this depends on the quality of the equipment. In this case the Note has plenty of strength to drive it since it's designed for headphones, but it may have a noisy output.
Ideally you should have your output (from the Note) as high as possible, and your amp gains as low as possible. This will provide you with the lowest noise since some noise in cables is unavoidable (but shouldn't really be a problem in most setups). Since you are controlling your volume with the Note, this probably isn't possible unless you use some sort of volume control built into something after the Note.
Here are some things you can try:
1. Not sure what kind of amps you are using, but make sure they have a decent signal/noise spec. It should be >90 dB. If not, you need better amps. Car audio amps are usually not that great in this respect. Some are really horrible. With a normal head unit, you can get higher output levels, so the amp gain can be lower and this isn't as important as it is with your setup. In your setup the Note doesn't have very high level outputs, so this is crucial.
2. You could turn your Note's volume all the way up and use a volume knob in the RCA cables. One like this should work http://www.amazon.com/dp/B003FPD3IS/...I1TQVH9XN9VOIG . If the white noise is coming from the Note (and not the cables), this will help, otherwise it will not. It will not make up for bad amps.
3. You might try just connecting one amp in the most simple setup (with a different cable) and see if the noise still persists just for trouble shooting. If it works, then something is wrong with your RCA wiring.
I have a strong suspicion the noise is coming from your amps. If not, it's probably coming from the Note. If it is coming from the Note, a USB DAC will help (if it's decent quality).