Alright so let's begin, I don't want to make this a long boring article so I will show you guys a step by step guide on how to do so, for both iOS and Android.
Steps
MAKE SURE YOU UPDATE THE VINE APP TO THE LATEST VERSION!
1) Open up the Vine app, and tap on the house icon followed by your "Profile"
2) Afterwards tap on the big "Settings" button you cannot miss
3) Scroll down just a bit and tap "Your content"
4) Turn the slider on or off to either your posts are protected* or sensitive posts**
* - Only your followers can view your posts
** - Your posts may contain sensitive material
Enjoy
~techungry1