Twilio Content Pack 50 message limit (pagination)

You can use the twilio API in a python script to get the full data. 

If you want this to be available on Power BI Service, however, I believe you will need to run the query through a personal gateway as well as hard code the Twilio credentials (which is, generally, not a good idea) into your script as is discussed in regards to the Zendesk API here. 

You will also need to install the Twilio API Python SDK

You could also try to construct the API request in an R script, but using the Python SDK is much easier. This works for me:

from twilio.rest import Client
import pandas as pd


account_sid = 'YOUR_ACCOUNT_SID_HERE'
auth_token = 'YOUR_AUTH_TOKEN_HERE'
client = Client(account_sid, auth_token)

messages = client.messages.list(limit=51)

frame = pd.DataFrame(columns=['sid','date_sent','account_sid','to','from','body','status',
'num_segments','num_media','direction','price','error_code','error_message','date_created','date_updated'])

for record in messages:
    frame = frame.append({'sid':record.sid,'date_sent':record.date_sent,'account_sid':record.account_sid,
    'to':record.to,'from':record.from_,'body':record.body,'status':record.status,'num_segments':record.num_segments,
    'num_media':record.num_media,'direction':record.direction,'price':record.price,'error_code':record.error_code,
    'error_message':record.error_message,'date_created':record.date_created,'date_updated':record.date_updated},ignore_index=True)