He has more or less the same powers as Tzeentch; he's omniscient and can alter destinies to create a new destiny (so nothing is safe unless he doesn't fuck with it) with little more than a thought (that's right, he can fuck up your life just by thinking about it, and since you are here reading this, he probably has). So yes, he's another Mary Sue of Chaos that always wins regardless because he already won unless he loses, which would only be because he wanted to. At the furthest depths of functional insanity, the afflicted become attuned to the mind of Amon 'Chakai. They scream warnings that HE COMES, while the more stable Wizards/Psykers of the settings watch him carefully waiting for his eventual move. Which would probably end all resistance.
He also has an army made up of the Daemons of all factions, because he's manipulated everyone to serve his whims. Yeah...
Amon 'Chakai was most likely dropped in later editions because he makes Tzeentch irrelevant, because "I did it 30k ago" only really works for one individual on the same side without causing an echo. GW could've kept him in the game just filling the same role as Kairos Fateweaver with a different name, but GW isn't that clever.
Still canon, bitch! In the 8th edition of the Chaos Warriors, the Sword of Changes is mentioned, which was forged by a demonic warlord (it is strange that they did not call him simply the Greater Daemon or Lord of Change) and the air around this blade is constantly changing: at one moment the blade is wreathed with the scent of sweet perfumes reminiscent of Slaanesh, only to be replaced a heartbeat later with the stench of rot and decay of Nurgle. An eye-blink later and the air around the Sword of Change shines with multicolored hues of Tzeentch before being surrounded in a haze of misted blood associated with Khorne. As already mentioned, Amon 'Chakai is so powerful that he controls the demons of all factions, so it is not surprising that he was able to forge a blade that is associated with all Chaos Gods.
3e Fantasy Stats
In the original Champions of Chaos splatbook for Warhammer Fantasy, Amon'Chakai is a Lord of Change special character who costs 855 points and must be accompanied by a retinue of at least 855 Tzeentch daemons. He can be the army's General if you want. For this huge price, you're getting a Flying character with Movement 8, Weapon Skill and Ballistic Skill 9, Strength 7, Toughness 7, Wounds 8, Initiative 9, Attacks 6 and Leadership 10. He causes Terror, has a 1+ Daemonic Aura save, and Hates any creature of Nurgle -- daemons of Nurgle, creatures with the Mark of Nurgle, or units lead by a Champion of Nurgle, he hates them all! He also has three unique Daemonic Rewards... which, due to the way this edition works, have to be paid for in addition to his basic cost, although at least his Master of Sorcery and All Seeing Eye can be taken by other characters as well.
- The Hand of Destiny: Designate one enemy model; the chosen target is cursed with death, and for the rest of the battle, all hand-to-hand and shooting attacks against this model hit automatically. This effect lasts even if Amon'Chakai is killed. Costs 30 points.
- Master of Sorcery: Costing a whopping 250 points, this daemonic reward turns its bearer into a level 5 Wizard who can draw 5 spells from either the Tzeentch, Dark Magic or Battle Magic spell decks.
- All Seeing Eye: Costing 50 points, this daemonic reward lets the player choose a single enemy model at the start of the game, after both sides are deployed. The enemy player must reveal all equipment, magic items, special abilities and spells that the target has -- and if the target is a Wizard, they lose a random spell and cannot use it during that battle, although their level is unchanged.