If you have ten files, you can create ten dataflows and have them run in parallel OR have ten different packages and call them in parallel with a master package. Or a combination of both. The problem you are facing is that if your download errs at any point you would have to start over. So it is not a bad idea to import into a raw file locally and then have the next dataflow do the transformations sourcing from the raw file.

I am curious, are any of these file you are importing going to have duplicate rows across batches? If you can find a way to only import what you need that could be a big resource saver by not moving millions of records across a network by parallel transactions.