Notice that verse 8 gives the time setting of Revelation 14:11: It concerns the impending fall of "Babylon." Verses 9 and 10 state:
If anyone worships the beast and his image, and receives his mark on his forehead or on his hand, he himself shall also drink of the wine of the wrath of God, which is poured out full strength into the cup of His indignation. And he shall be tormented with fire and brimstone in the presence of the holy angels and in the presence of the Lamb.
Obviously, this takes place at Christ's second coming.
Those who have a part in this system of "Babylon," and who receive this frightful punishment from Almighty God, have "no rest day or night" as long as they remain in that land falling under God's wrath. They will either have to flee that area and seek God's mercy or be tormented by fire and sulfurous fumes until they perish.
Notice that verse 11 says, "The smoke of their torment ascends forever and ever," not that these individuals will be tormented forever in an ever-burning hell. God is not a sadist who wishes to torment His enemies perpetually. He clearly says in Romans 6:23 that "that wages of sin is death," and that is what is being described here: a death of well-deserved but short-lived agony.
The Bible plainly teaches that flesh and blood is subject to combustion and death (Hebrews 9:27; Genesis 3:19; Ecclesiastes 3:20). Malachi 4:3 says that in the end the ashes of the wicked will be under the feet of the righteous. The wicked will be destroyed and will die that death, the second death, from which there will never be a resurrection (Revelation 20:6, 14).