Is there a 'Messenger of the Gods' figure in Egyptian mythology?
While Thoth is often equated with Hermes, he seems to be more of a keeper of secret wisdom than a messenger.
Is there any such figure in Egyptian mythology?
The Greeks are the one who actually referred Thoth as Hermes. You have that said a second zone god, Aput which is, technically, your answer but Aput (not Apet... Aput, Apet is a goddess) is not THAT famous. In most stories texts are written and send by Thoth himself. so while Thoth does not cover the messenger part, per se, the Greeks saw with reasons the connections. At its root Egyptian society already had a "gods talker" with the pharaoh. Egypt was a religious kingdom not a bunch of city-states.
Other than the little known Apt, arguably the closest direct Egyptian analog to Hermes would be the synthetic deity Hermanubis. Who is, as you might guess from the name, the result of combining of Anubis and Hermes. He only emerged in Ptolemaic Egypt however, so a little on the late side of ancient mythologies.
The combination was rooted in the role of Anubis as the conductor of souls, a trait he shares with Hermes. However Anubis was also the messenger of Osiris in the Book of the Dead, and, according to E. A. Wallis Budge, the "chief envoy of Ra". The ancient writer Apuleius likewise calls Anubis the messenger of gods, although that's probably the Roman projecting attributes from Mercury or Hermes.
- Budge, A. E. W. The Papyrus of Ani: The Theban Recension of the Book of the Dead. The Medici Society, London 1913.