Mormonism defines "prophecy" loosely as "what is revealed through the Holy Ghost". That is my own definition, but it comes from the Bible Dictionary that is included as a part of the scriptural helps that are in the KJV Bible that the Church publishes. Under "Prophet", it says:
"In a general sense a prophet is anyone who has a testimony of Jesus Christ by the Holy Ghost, as in Num. 11: 25-29; Rev. 19: 10."
From Numbers 11:25-29:
and it came to pass, that, when the spirit rested upon them, they prophesied, and did not cease ... (and Moses said) would God that all the Lord’s people were prophets, and that the Lord would put his spirit upon them!
From Revelations 19:10:
I am thy fellowservant, and of thy brethren that have the testimony of Jesus: worship God: for the testimony of Jesus is the spirit of prophecy.
Given this definition, Mormonism has no problem accepting non-Mormons as "prophets" in that most expansive sense - as someone through whom God chooses to speak through the Holy Ghost. In fact, this is very consistent with the OT perspective, when numerous "prophets" lived at the same time and seemed to come out of the woodwork prior to great calamities. There is a difference between that, however, and the "calling" of someone to the "Priesthood office" of prophet.
Those who have been called and ordained as prophets and apostles are "set apart" to prophecy (to share the word of God as moved upon by the Holy Ghost). They aren't "perfect" (complete and whole and fully developed) in this responsibility (meaning they aren't infallible), but they do "read the signs of the times" and share their inspiration with the world as a result. That also is why, frankly, we should have little problem letting go of things that were said in a different time than our own (or even in a different culture concurrent to our own) - since what God communicates with his children can change according to the needs of the people at any given time or in any given culture. He also communicates according to their willingness to listen.
For example, if highly addictive substances are unknown in one society, there is little reason to expect God to prompt a prophet to speak of them; if, however, those substances exist or will be introduced shortly in another society, there is every reason to expect prophets in that society to mention them. This also explains why the Jewish priests in
at the birth of Jesus had no idea about the prophecy regarding the star, while "wise men" from the east did know of it. One group was open to being told about it; the other group was not - so, apparently, God simply didn't inspire any prophets from that area to mention that upcoming sign. Jerusalem