It may seem like it takes a while after you click 'submit', but don't worry your data is en route to your Amazon account.
Once you have uploaded your parts and fitments, and have submitted them to Amazon, the processing time will depend on how much data has been sent. It can take anywhere from 24 hrs. to a couple weeks. Remember, they have to validate the data and ensure that all the part mappings are valid.
After initial submission, you'll receive an email from Parts Connect with a process report including a data processing number. For information regarding this submission, you will need to contact an Amazon representative directly using the processing number to check the status. In order to verify that your data has been published, you will need to go to the Parts Finder on Amazon and look up a vehicle that your part fits and check to see if it appears.