That PAM8403 is a class D amplifier so its output signal will be PWM (switched). So you need to filter the signal. Also, on average it will be half the supply voltage (as it switches between Vdd and ground) so you need to AC couple the signal as well as the LM3915 expects a ground referenced signal.
That the outputs af the amplifier are differential does not matter much, you can just use only one output. The other output carries the same signal but inverted (upside down). If you'd connect a speaker with a series capacitor between any of the outputs and ground, you'd hear the same signal (although inverted but your ear cannot detect that, only relative to another signal).
You could try this:
simulate this circuit – Schematic created using CircuitLab
C1 is the AC blocker cap
R1 and C2 are a low-pass filter with a cutoff frequency of around 10 kHz
This is just a suggestion and staring point. Don't blame me if it doesn't work as expected ;-)
You could also consider using the input signal of the PAM8403 as a signal for the LED driver. Optionally with a simple audio amplifier. A basic LM386 audio amplifier module will do the job and these are cheap.