You can get it from the Report Server Database.
All the Reports deployed to the Server get stored in Catalog table in Binary data format and we need to convert it into XML file. And that XML file will be your actual Report.
Use the following query to retrieve a list of SSRS reports with the source. Rename the xml to rdl and should be able to upload the rdl file on to the new report server.
USE ReportServer GO SELECT Path, Name, SourceCode = CAST(CAST(content AS VARBINARY(max)) AS XML) FROM ReportServer.dbo.Catalog WHERE Type IN (2,6) ORDER BY Path, Type, Name