Access private access storage files and pass file name as parameter to REST API

We have a Data Lake Storage Gen 2.0 account with a container named "FILESTOUPLOAD" containing several csv files. Container "FILESTOUPLOAD" is NOT publicly accessible. Need to upload the csv files to a private cloud which exposes REST APIs to import the files. The API that is exposed to import data  expects file path or URI endpoints to be specified and also, the request to be sent as ‘form-data/multipart’ mode. How to achieve this as files in data lake container is NOT publicly accessible?