Why isn't this AM Demod GNU Radio flow graph working with different sampling rates?
In order to make the filter calculations easer, you should specify its sampling rate equal to the source's. Assume that:


$D$ is the filter's decimation factor
$f_s$ is the source sampling rate
$f_c$ is the filter's specified cutoff frequency
$f_f$ is the filter's specified sampling rate


The actual cutoff frequency from the point of view of the filter's output, $f_a$, is calculated as: $$f_a=\frac{2Df_c}{f_f}\frac{f_s}{2D}=\frac{f_cf_s}{f_f}.$$ This is because the filter doesn't care what the actual sampling rate is; what it needs to know is the cutoff frequency as a fraction of the normalized Nyquist frequency, which is $2Df_c/f_f$ after accounting for the decimation.

In your first flowgraph, the actual cutoff frequency is $5\cdot256/64=20$ kHz, not 5 kHz (the same problem occurs in the second flowgraph; in the third, the cutoff is 25 kHz). If you specify the filter sampling rate equal to the source rate ($f_s/f_f=1$), then your signal will actually be filtered at 5 kHz.

You also need to make sure that the product of the source sampling rate, times all your interpolation, divided by all your decimation, is equal to the sink sampling rate. In the third flowgraph, the sampling rate into the sink is 16 kHz, not 48 kHz.

Having said that, I think there's another problem in your flowgraph. I assume that you're demodulating AM DSB-LC. If the RTL-SDR device is centered exactly at the carrier frequency, then you only need the low-pass filter; no complex to mag conversion is necessary. You only need to keep the real part of the signal (send the imaginary part to a null sink -- you can do this right after the RTL-SDR and save some computations).

You only need to do envelope detection when the AM signal is not in baseband. In that case, you calculate its absolute value and then low-pass filter it. You also need a final high-pass filter to eliminate the DC bias present at the LPF output.