The burden voltage varies linearly with the current being measured. The only constant is the shunt resistance for a particular range (Ohm's law). So it should be given as a ratio of voltage versus current, ie: mV/mA. A burden voltage figure by itself doesn't mean anything, unless it is referenced (by convention) to the full current range under consideration.
The burden voltage of the Fluke 87V, for instance, on the milliamp range, is 1.8 mV/mA.
As an example, if your multimeter mA range 5ohm shunt is placed in series to measure the current flowing through a 25ohm circuit powered with a 3V battery, you will measure a current of 100mA instead of the actual 120mA, if the meter was not part of the circuit.