I managed to do this but not with RESTful services. The steps were as follows:
1. Use SDK to identify BOA file in FRS.
2. Copy source file (XLSM) to a workspace so as not to touch the original.
3. Unzip the XLSM. Java and most zip tools can do this.
4. Read XML file ..\xl\customProperty2.bin. It's an XML (char set UTF_16LE) that contains the data-sources.
A similar process can be used for identifying Design Studio data-sources but in this case the source for the report is an XML.
Good luck