Knowing this first, that no prophecy of the scripture is of any private interpretation.
This verse has been used by many people to argue that Mormonism's unique teachings are wrong - in that they claim those teachings are "private interpretations" of scripture. The following is my view of this verse, focused strictly on a) understanding what the verse actually says (parsing the words for the most straightforward meaning) and b) looking at the historical context of the Bible and the verse itself.
1) Joseph Smith took care of it by changing it - to "no prophecy of the scriptures is given of any private will of man." So, he interpreted it privately. (*grin*) I actually like his change a lot.
2) If you take a look at our canonized scriptures (and even just the Bible) there are plenty of things that are "scripture" but not "prophecy" and many other things that are not "scripture" in the purest sense of the word (God's word to man). There are very good questions regarding Biblical authorship and arguments to believe that prophets weren't (and aren't) infallible. Thus, it is important to point out that 2 Peter 2:10 does not apply to the entire Bible but, instead, only to "prophecy of the scripture" therein.
3) The parser in me focuses on the words and points out that the verse as written in the KJV doesn't rule out the readers interpreting scriptures; rather, it says scriptural prophecy isn't "OF" (generated by) personal interpretation. So, the most straightforward parsing means:
"Anything that is true prophecy recorded in the scriptures doesn't come from the individual; rather, it comes from God."
4) It's also important to realize that what Peter saw as "scripture" might have differed radically from what we have as "canonized scripture" now, especially since the Bible wasn't organized and canonized for hundreds of years after his death.