What is Amos 9:13-15 a prophecy of?
About Amos 9, this is a prophecy of God coming to bless his people after he has earlier judged them (see earlier in Amos, where God warns them about judgment because of their unrighteousness). Most likely he is referring to sending Judah into exile (Amos preaches to Judah) in Babylon when Nebuchadnezzar defeated them and their return to the Promised Land in 536 BC and the rebuilding of the temple in 516 BC. The wording is a symbolic representation of how God would bless them.
What happened when Judah was sent into captivity in Babylon and later a remnant was set free and lived again in the Promised Land is a foreshadow our our own captivity to sin and our being freed from sin by Jesus. We, too, are a blessed remnant of God. In Revelation being in Babylon is symbolic of being captive to sin and being freed from Babylon is symbolic of salvation. This imagery is also found in early church father writings. So, indirectly, Amos 9 is a prophecy of our being saved as a remnant from salvery to sin, but I believe it is a direct prophecy of the restoration from Babylon.