Given hardware specs: How do I calculate the data bandwidth [bits/s] of this system?
Each channel produces 128 samples per second.

Each sample has 14 bits of information (but maybe 16 bits are transferred somewhere? that's not clear).

There are 14 channels.

So it looks like the total bandwidth is

$$14\times14\times128=25.088\mathrm{kbps}$$

Maybe 28.672 kbps are actually transferred, depending whether those 2 "discarded" bits in each sample are discarded before or after transferring them.

Edit

As Dave points out, there is a note that indicates the internal sample rate is 2048 Hz (really, 2048 sps). Given that the 14 channels are sampled sequentially, this indicates that likely there are 2 unused channel sampling slots, ans so the overall bandwidth being generated by the sampler is 

$$16\times16\times128=32.768\mathrm{kbps}$$

Of this, two sampling channel slots and 2 bits per sample are not useful data. Whether they are actually transferred over whichever interface you are asking about is not clear.