Whenever you create a new Subscription in Sql server reporting services, a new job is created under the Sql agent as shown in the figure below.
You can use the msdb.dbo.sp_start_job procedure to start the job. In SSIS create a new SQL task and run the job wherever required
exec msdb.dbo.sp_start_job @job_name = 'JobName'
For more information about sp_start_job please refer MSDN
