Let All Mortal Flesh Keep Silent/Silence is not really a hymn about the second coming. Its origins are the Divine Liturgy of St. James (an Eastern rite). Its place in the liturgy is after the catechumens and other non-initiated have left (after the Gospel):
The Singers begin the hymn Let all mortal flesh keep silent**, slowly and melodically.**
Let all mortal flesh keep silent, and with fear and trembling stand. Ponder nothing earthly-minded, Let all mortal flesh keep silent, and with fear and trembling stand. Ponder nothing earthly-minded, for the King of kings and Lord of lords advances to be slain and given as food to the faithful. Before him go the choirs of Angels, with every rule and authority, the many-eyed Cherubim and the six-winged Seraphim, veiling their sight and crying out the hymn: Alleluia, Alleluia, Alleluia.
After the holy Gifts have been placed on the holy Altar and before they are covered with the Cloud, the Priest says…
So the purpose of the hymn is to call to attention the imminent (in their case) Real Presence; so its use during Communion seems appropriate, although the consecration has already taken place.