Apparently, updating the Linux kernel with a pre-build image from Robert C Nelson on the beaglebone black is extremely easy. The scripts to do so are already installed available in the standard debian build I used.
Following these instructions on a clean debian install, gave a running debian with a 3.16 kernel (I used the testing image).
The LogiLink wireless dongle works out of the box with that kernel, no fiddling with the driver was necessary.