Details and Conditions
From Bungie's Help articles:
"Players may create videos using Destiny gameplay, which may be uploaded to third party sharing services like YouTube. If a chosen video-on-demand service enables players to monetize content, 20% of the content within the video must have been created by the player. Examples of what “player created content” may be defined as include custom commentary, animations, graphics, or gameplay."
"Streaming gameplay is another viable form of sharing community-created Destiny content. Services like Twitch enable players to monetize content via subscriptions or donations."
There are no explicit rules against streaming only for paid subscribers on Twitch. I would recommend contacting the developer for certain just in case as an extra precaution.