You could also set an Agent job to periodically monitor the status of the File Share subscription, using the Subscription table in the ReportServer db. Then, upon successful completion and whatever other parameters you wanted, it could kick off the second Email subscrip.
If you absolutely HAD to use *only* SSRS, then you might be able to get away with a similar approach as outlined HERE
, but instead your EXISTS clause would again read from the Subscriptions table on the ReportServer db to find a successful saving of the FileShare subscription file. You would probably have to run it like every 5 minutes starting when your FileShare subscrip fires, and then have it go for some amount of time until you're sure the FileShare subscrip would be done.
I've never tried it before, I would just use SSIS, but off the dome it seems like it might work?