Multiple audio inputs driven by one MP3 player output
It is always good to check the datasheet of a component when you are after information like this. The important thing to know is its input impedance, if that is high, then there is little or no problem connecting a couple of them in parallel. You'll have to develop a feeling for what is high and what is low. Sometimes you even find other useful information about the chip, eg. did you know about "power supply pumping" and how to address that? Interesting topic if you are driving these chips in parallel on the same supply.

Anyways, I admit input impedance is a bit hard to find in the datasheet, it is discussed in the chapter called "Gain setting via GAIN0 and GAIN1 inputs". You may notice some degradation at higher gain settings where the input impedance drops to about 9kΩ. When driving the amps from a headphone output, there should be no issue driving such low impedance. Notice that when driving multiple amplifier in parallel, the MP3 player will see an impedance 9kΩ/N where N is the number of parallel amps. 

I'd start to frown when the parallel impedance drops below 1kΩ (9 in parallel) and I'd start to worry when it drops below 100Ω. Most MP3 players are designed to drive 32Ω headphones.