Following are the steps in the tutorial on how to quickly delete all SMS on Iphone:
1. Open the Messages application on the Iphone,
2. Press the Edit menu located in the upper left corner,
3. Select the Select Messages menu,
4. Then, press the tick in the circle column located on the left side of the SMS and drag or drag it quickly from top to bottom using your 1 finger,
5. If all SMS have been checked, then all you have to do is press the Delete menu which is located in the lower left corner,
6. Done.