accuracy shunt resistor beter than 0.1%?
You should expect to have to apply your own calibration to build instrumentation to this sort of level - you can't just expect to put a bunch of bits together and achieve fantastic precision/accuracy.

You will probably find some fairly simple slope-and-offset linear calibration is all you need for this case, though ammeter shunts can be tricky beasts.  For a start you need to make sure you are definitely measuring the voltage across the shunt, and not seeing a lot of ground lift happening elsewhere in the circuit.

Also think about the temperature coefficient of the shunt resistor - you might find the accuracy of your reading depends on how long the load's been turned on for...