-Amil teaches that they millennial reign is in heaven. It began in the 1st century when Jesus ascended to heaven to sit on his throne and was given all power and authority. Christians reign with Christ when they die and go to heaven in what is called the intermediate state. 
-Amil teaches that the earthly reign is the new earth that comes after the millennium, not the millennium itself. 
-Amil teaches that Satan was bound in the 1st century and that binding of Satan was the same one spoken of in Rev. 20 for the millennium. Satan is not bound from making trouble in the world, but from preventing the gospel to go out into the world for others to receive. 
-Amil teaches there is one resurrection, followed by the final judgment, followed by the new earth. 
-Amil teaches the 1000 years is not a literal 1000 years, but incapsulates the whole church age. 

1st let’s address 2 presuppositional teachings that create inconsistencies with Amil.

Presupposition #1 - Historicism
While there may be a few people out there that hold to both Amil and Historicism at the same time, I believe it to be an inconsistent position to hold. Daniel 7 reveals that the saints received(vs18) and possessed(vs22) the kingdom AFTER the destruction of the little horn. In the Historicist view, the little horn is the Papacy. So if this possession or receiving of the kingdom is the start of the millennium, then the Amil teaching of the millennium starting in the 1st century can not be true. If the saints received and possessed the kingdom after the Papacy was destroyed, this means that before had they had not yet possessed or received the kingdom. How then could they be reigning with Christ in a kingdom they had not yet received or possessed? Historicism and Amil are incompatible positions to hold at the same time. 

Presupposition #2 - Soul Sleep
The other incompatible position to hold with Amil is the doctrine of soul sleep, which stands in direct opposition to the traditional doctrine of the immortal soul. The Bible teaches not that we have a soul, but that we are a soul. And the soul can die. Read the following page to understand this further: What Happens When We Die?. Amil does not explicitly teach the immortal soul doctrine, but is does presuppose it. Amil teaches that when we die, we go to heaven(or hell) and reign with Christ and that that is the millennium. There are some variations, but none of which allow for soul sleep. It is 100% inconsistent to hold to both teachings at the same time. If soul sleep is true and the doctrine of the immortal soul is false, the Amil falls with it.