There is no corroboration that Satan will be bound for 1000 years in the future and then released to deceive countless billions who have sat under the unparalleled righteous rule of Christ on earth.
But there is multiple scripture to support the Amillennial position. Matthew 12:22-29, Mark 3:11, 23-27, Luke 10:18-19, Luke 11:20-22, John 12:31-33 Colossians 2:13-15, Hebrews 2:14-15, I John 3:8, Revelation 9:1-11, Revelation 12:7-9 and Revelation 20:2 prove Satan was cast out, bound, defeated, incapacitated, divested of power, disarmed, brought to naught, undone, stripped and spiritually imprisoned through Christ's sinless life, atoning death and triumphant resurrection.
Satan has not been rendered immobile or inoperative but is limited in his power, kingship and influence by being defeated on the cross. He is like a dog on a chain. He is shackled.