Still not clear in which cube you want to know request ID: in BPC cube or in staging cube? But really request ID doesn't have any meaning in rel-time (BPC) cubes. In basic cubes it plays a role of some unit of work, like a single load. In BPC cube records are grouped in a request just based on number of records processed. Hence knowing request number of something doesn't provide you any information.
If you want some process to put records in a separate request you should close open request, run your process and close open request again. Then if nobody else is posting anything at same time you have a chance to know request IDs of your records.
Otherwise - no way.