My office has the 2012 version of LabVIEW which uses the 2012 version the Report Generation Toolkit. If we buy the RGT on the NI website will the serial key work with the 2012 version? I don't see any option to purchase older versions of the RGT.
The answer is "Probably not". It is not so much that the License is "wrong" (I assume that is what you meant by "serial number"), but if any of the VIs and functions in the 2015 RGT have been compiled for LabVIEW 2015 (or 2014, or 2013), you will not be able to open them with LabVIEW 2012.
I recommend you get in contact with your NI Sales Team and discuss this with them. An alternative "solution" is to purchase the LabVIEW 2014 or 2015 Professional Development System, which includes the RGT.