The Facebook iOS app just got updated to version 5.4, and now officially added the voice messages and video recording right within the app.
What's New in Version 5.4
Share your moments with voice messages and video recordings right in the app.
• Send voice messages when you have more to say
• Record and share videos right from the app
• Share and connect with your favorite places using the improved Nearby tab
As far as I know, the Android app has not been updated yet.