Accessing your uploaded files via API
Because your uploaded file details are stored in your Shopify order data (under line item properties), you can use the Shopify API to access them. You can also create webhooks to be notified when new orders are created, and these include line item properties that contain links to your uploaded files. To access the Shopify API you need to create either a custom app or a private app.
You can add a direct link to the file to your line item properties using that option in UploadKit field settings, which makes these integrations significantly simpler. Your standard file link will lead to a preview page where you can download the file -- the direct link connects to the file itself.