The angel is obviously speaking for God—they are not the angel's witnesses but God's! We should note the use of the English possessive "My," which suggests both personal ownership and affiliation.
However, the Greek reads more literally, ". . . the two witnesses of me." While this rendering also imparts the idea of possession, it adds a vital element: that the Two Witnesses testify about God Himself. They are God's direct representatives in the crucial last years of man's civilization. And they represent Him, not just in words, but in everything they do during their prophetic ministry.
In other words, these two men are not run-of-the-mill Christians by any means! Not a single word of censure is aimed at them in either Revelation 11 or Zechariah 4. They will be model Christians, followers of Christ and His righteousness to such a degree that when the people of this world observe them, they will see human reproductions of the life of Christ. In much the same way as Jesus represented the Father during His physical life, so will the witnesses represent Jesus during the Great Tribulation and the Day of the Lord (see John 14:9). While they will not be perfect, they will be men of godly character and virtue.
It is no wonder, then, that they attract the wrath of Satan and the Beast, as well as the hatred of the whole world! Just as Jesus was opposed, mocked, persecuted, and finally killed, so will these men draw the fire of the anti-Christ, end-time population of earth. Thus, Christ endues His two prophets with power to preach, to plague, and to defend themselves against harm (Revelation 11:5). In order to survive their mission during a time of Noachian-type violence, God will give them the tools and protection to reveal Him for a final time as a witness before Christ intervenes in world affairs.
Therefore, we should not be looking necessarily for great signs and wonders being done by two prophets, as that activity will likely be confined to the final three and a half years. By that point, it will be obvious to the enlightened who they are. As Revelation 11:9-10 suggests, by the time they are finished with their work, the whole world will know who they are.
Instead, at this time we need to be looking for Christ-like servants who are fulfilling the type of the two olive trees—feeding the churches through their Holy Spirit-inspired works—and who are focused on "measur[ing] the temple of God, the altar, and those who worship there" (Revelation 11:1). They will be intensely laboring to achieve the equipping of the saints (Ephesians 4:12) for the terrifying days to come and the return of Christ.
Who the Two Witnesses are has not yet been revealed, and how long we have to go before the time of their appearance no one knows. However, in looking for them, we need to concentrate on what Scripture reveals so that we might properly identify them. Ecclesiastes 3:11 in the Moffatt version declares how God works in these matters: "He assigned each [thing] to its proper time, but for the mind of man he has appointed mystery, that man may never fathom God's own purpose from beginning to end." God will make them known when their time has come. So, wait and watch!