This is definitely not an answer to your problem. It more like a long comment.
The main question for me is: why do you need to get that uncertainty measurement for sensor A?
A few points of note:
Each sensor (or measurement line) has its own uncertainty values. I.e. the datasheet reference value of uncertainty for sensor B, is not necessarily the same that you would find if you calibrated that sensor in an accredited laboratory.
A good reference for generic uncertainty is "Guide to expression of uncertainty in measurement ". This is a generic document that provides useful procedures and directions.
With respect to your problem (although its not clear what you are trying to achieve), to measure the uncertainty of a proximity sensor I would have expected that the standard procedure would require the use of fixed distances (not the measurement from another sensor).
The uncertainty of sensor A ($u_A$) in that context would mean to me that for a fixed distance, sensor A would return a value with a $\pm u_A$. And yes you can compare that to another sensor, but its more definitive if you use a fixed distance (at least IMHO).
I have the above perspective because I have the following experience which (at least in my opinion) I consider relevant/comparable. My experience was with checking the calibration of an anemometer in wind measurements with a backup anemometer in a ISO-17025 accredited laboratory (in another lifetime). In that case a calibrated anemometer would be periodically be used to check that the tested anemometer has not suffered a significant change in calibration parameters. However, in that procedure, the tested anemometer was not considered recalibrated, and although the uncertainty of the measurement is calculated it is not used outside of a "GO, NO-GO" decision type system.