I'm trying to join my friend's world on iOS from my Android phone, and I'm having a hard time doing so.
Can an iOS device join an Android device using the newly added Xbox multiplayer system?
Yes, it should be.
As stated on this blog post and this news article, the Xbox multiplayer system is cross platform:
http://news.xbox.com/2015/09/08/games-minecraft-pocket-edition-and-win10-edition-update/
what’s even cooler is the cross-device multiplayer that is now possible with Xbox Live. Starting now, you can easily connect with your Xbox Live friends for online multiplayer games, regardless of whether they are playing on the Windows 10 Edition or a supported mobile device.
http://www.polygon.com/e3/2016/6/13/11922908/minecraft-cross-platform-e3-2016
Called "The Friendly Update," it will bring dedicated servers across the platforms. Windows 10, Android and iOS users can currently play together