There are some issues that you will face with this solution.
Let's assume that you have the packages developed & deployed. You have 12 SQL Agent jobs created. You have built a client app that connects to the relevant SQL instance and runs sp_start_job when a certain button is clicked on the form.
Your first issue is user feedback. sp_start_job runs asynchronously and therefore you cannot easily monitor the progress of the job from the client app.
When the job completes, how will the user know?
If the job goes wrong, how will the user know?
What happens if several users click the same button?
Do you want to give your users rights to start SQL Agent jobs?
How do you prevent the same file being processed more than once?
(OK, the last one is easy: archive it after processing.)