You can write your own faxing app using the Fax API. Check out the dev guide and choose your programming language to see how it can be implemented.

For sending to a distribution list, just load the recipients number into an array then iterate the array to send one by one.

If you see the Fax API here: https://developers.ringcentral.com/api-reference/Fax/createFaxMessage

there is an array in the request, To field where the Fax message will be send

eg:

{"to":["3545454567","65656565677"]}

This array is the collection of phone numbers where the Fax will be send automatically at a same time.

So, you don't need to repeat the Fax API call one by one to send to each number