1. The plot of Revelation 16-20 is straightforward. After devastating aerial bombardment (16), Babylon is reduced to smoldering rubble (17-18).
Incidentally, if you wish to understand the fulfillment in futuristic terms, you could view it in terms of orbital weapons.
After heaven rejoices over the downfall of Babylon (19:1-10), Jesus returns. He defeats the armies of Satan on the battle field (19:11-21).
Satan is taken into custody, as a war captive. The abyss is a subterranean POW camp (20:1-3).
You have the "Millennium" (20:4-6).
Satan is then paroled. He raises another army, is defeated, and cast into the lake of fire (20:7-10).
BTW, what does it mean to say he's "released"? Did he escape? Was that an inside job?
2. In traditional, Augustinian amillennialism, the Millennium represents the church age. However, that doesn't fit the plotline. In the plot, the Millennium is just one phase in the history of the church. It hardly covers the entire period.
More recently, some amils construe the Millennium as the Intermediate state for Christians. That has more going for it than the traditional, Augustinian interpretation.
To some degree, the premil reading is more straightforward insofar as it tracks the actual sequence of the plot. However, that simplicity is deceptive. Premils add a lot of subplots to 20:4-6 by using that as a framework to place the fulfillment of various OT and NT endtime prophecies. They attempt to correlate Revelation with other prophetic notices in the Bible, but that clutters the plot.
In addition, Revelation isn't a historical narrative like the Gospels or Acts. Rather, it's more like historical fiction. Although it refers to some real people, places, and events, it also contains a lot of imaginary material. So we can't just assume the storyline mirrors a historical sequence. In another respect, Revelation is the ancient equivalent of superhero comic book flicks, with their surreal cityscapes, their heroes and villains with paranormal powers.
Furthermore, there's the problem of where Satan finds a recruiting pool to raise another army, of hyperbolic size, after his army was annihilated the first time around. That's because Revelation rhetorically bifurcates the battle of Gog and Magog into two stages, separated by the millennial interval.
3. Then there's the question of what the binding/loosing of Satan signifies. What's the real-world analogue? The binding/loosing of Satan and the deception of the nations are corollary. There's some conceptual relationship. So what does it mean for Satan to deceive the nations? How does Satan deceive the nations? And how is he bound?
i) In Rev 12, we have a studied anachronism. Satan's power is broken by the Crucifixion, Resurrection, and Ascension of Christ. That's depicted in terms of civil war in heaven, where Satan and his cohorts are expelled. That uses imagery from the prehistoric fall of Lucifer to represent a historic event. That should warn is to be careful about the "timing" of the imagery in Rev 20:1-10. We need to guard against synchronizing what might be an intentionally anachronistic description.
ii) With that in mind, the binding/loosing of Satan isn't necessarily a one-time event. It might be something that happens intermittently at different times and places during the course of church history.
ii) In Revelation, one way Satan deceives people is through heathen witchcraft. Paganism and witchcraft go together. Not only does Revelation use that terminology (9:21; 18:23; 21:8; 22:15), but the False Prophet is a sorcerer (13:13-15) who uses witchcraft to delude unbelievers (19:20).
On this view, one way Satan might be bound is when heathen witchcraft is banished. Or when Christian prayer trumps sorcery.
iii) Apropos (ii), Dan 10 might supply some conceptual background material for Rev 20. Daniel's prayer is impeded by a territorial spirit until the Archangel Michael intervenes. Not coincidentally, the Archangel Michael is Satan's nemesis in Rev 12. And not coincidentally, it's another angel (possibly Michael) who is Satan's nemesis in 20:2.
So another way in which Satan is bound may be when Christians pray (cf. Rev 5:8; 8:3-4), and God answers their prayers.
iv) Apropos (ii), the binding and loosing of Satan might correspond to possession and exorcism. Possession, paganism, and witchcraft go hand-in-hand. Demonic spirits delude unbelievers through signs and wonders (e.g. 16:14). Presumably, that involves possession. Sorcerers are demoniacs–demonically empowered. The notion that exorcism binds the Devil goes back to the Gospels.
I surmise that the binding and loosing of Satan picturesquely depicts in one big climatic battle what is more often many spiritual squirmishes in the course of church history, as Christian pray, perform exorcisms, and banish pagan witchcraft. But until the final battle, there's ebb and flow.