Deleting the conversation on iPhone is easy but deleting an individual SMS from the thread requires a little bit more work.
 

Also See: iPhone 6’s Big Screen Concept
 

Here’s how to do it: 

Select an individual message you want to delete by long pressing on it.This will bring up a “Copy More…” menu. Then select ‘More’ and that message will be get checked. You can also check any additional message you wants to delete and then select ‘Delete All’.

That’s it!