One possible issue with tapping into the car's electrics, especially the supply to the indicators themselves, is that it might make the BSI think there's something wrong and throw a wobbly. Solutions to this usually come under subjects such as how to add trailer or caravan light sockets, and I'm sure others will have elegant solutions on those lines.
In the mean time, a very simple method without touching the car's wiring at all, if you can do very basic electronics and have a small soldering iron, would be to place an LDR (light-dependent resistor) in front of your instrument cluster to detect when the indicator lamps in it flash, and wire it up to a small buzzer. Search the web for 'light triggered buzzer circuit' etc. One example:
http://www.learningaboutelectronics.com/...ircuit.php
All the components can easily be sourced on eBay etc.; as for the 3.5v power supply requirement I would test the circuit with a 5v supply, and if it works then you could power it from a cigarette plug USB outlet.
Other circuits are out there though. Example 2:
https://www.youtube.com/watch?v=iw2N6vrOC6I
Maybe there's even a gadget which does all this already.
If you could find two buzzers with different pitch noises, you could have two units, one for each indicator, so that you know which one is flashing. And of course your hazards would make an even more obvious noise! Which makes me think that you might also want to fit an off switch, for those times when we all have to sit on motorway hard shoulders for hours.
The LDRs themselves could be on long wires so that the rest of the setup can be placed elsewhere without obstructing the view of your instruments. What comes to mind is a small plastic box containing the works and the buzzer (holes drilled in it to let the sound out), with two long cables, one to your USB socket and the other with the LDR on the end. The box could be placed anywhere if the wires are long enough.
Experiment with fitting a tube over the LDR (a bit like the body of a telescope) so that it can only see the light from one indicator lamp in the cluster, to avoid false alarms.
One advantage to this approach is that the gizmo can easily be removed at any time, for instance if you sell your car on and want to put the gizmo in your new car.