In logic app we have Onedrive connector and Azure file storage connector. You can leverage different trigger/action according to your requirement.
If your requirement is when the file is created in onedrive then it should be copied to file storage then you can leverage When a file is created action and pass the output (content of the file) to Create file of file storage. Please note that there are limitation of connector and refer to connector document for more details.
In case your requirement is to copy few files based on user input then you can leverage Find Files in folder/Find files in folder by Path that returns the array of BlobMetaData. Now you can iterate through this array to get the content of individual file using Get file content/Get file content using Path and pass the output (content of the file) to Create file of file storage.
Feel free to get back to me if you have any queries or concerns or different requirement/scenario.