Sonic the Hedgehog 3 & Knuckles chronology and endings
From Sonic Retro
In Sonic 3, Sonic & Knuckles, and the combined Sonic 3 & Knuckles, the chronology of Sonic & Tails' story compared with Knuckles' is never spelled out explicitly. Does Knuckles' story, and his fight against Eggrobo, occur before, during, or after his confrontations with Sonic? How are the two routes through the game connected together?
While there is no single point in Sonic 3 & Knuckles that can be cited as definitive evidence of how and when the stories are linked, the game provides clues here and there which add up to a reasonable case. Let's review the evidence:
The Intro Sequence
The opening sequence of Sonic 3 takes place "many days" after the ending of Sonic the Hedgehog 2 and Sonic's plummet from the Death Egg - not immediatly succeeding it (note the lack of a booster on the plane in the ending of Sonic 2). As Sonic and Tails go to investigate mysterious happenings out to sea in the Tornado, Sonic transforms into Super Sonic, jumps off the plane and tears over the ocean, onto the beach of Angel Island, which has been pushed out of the sky by the weight of the crashed Death Egg. Knuckles punches out Sonic's Chaos Emeralds and the gameplay begins.
Hyper Sonic Ending
In the "best" ending of Sonic's story, after beating Doomsday Zone with all the Super Emeralds, Hyper Sonic shepherds the Master Emerald back down through the atmosphere, where he and the gem are picked up by Tails in the Tornado. They fly past Angel Island, dropping the gem off and enabling the island to rise back into the sky as Knuckles looks on happily.
Alternative Sonic Endings
However, if Sonic has not collected all the Super Emeralds, one of two possible alternate endings play, depending on his Chaos Emerald count. If Sonic has incomplete heptets of either the Chaos Emeralds or Super Emeralds, the game ends after the Great Eggman Robo and chase scene in Death Egg Zone. Sonic loses the Master Emerald while falling through the stratosphere, and the final fade-to-black shows Robotnik chuckling beside the Master.
However, if Sonic has exactly seven Chaos Emeralds (either by collecting them when playing Sonic and Knuckles on its own, or by never going into a Giant Ring and the Emerald Shrine in a docked S3&K), then he enters Doomsday Zone as Super Sonic, eventually returning the Master Emerald to Angel Island as in the Hyper Sonic ending. Now the final sequence shows an Eggrobo rising out of a pile of wreckage (of other Eggrobos). The implication seems to be that this is the robot which goes on to fight Knuckles in the echidna's playthrough.
Knuckles After Sonic?
If Knuckles' Eggrobo opponent only rises up after Sonic's end sequence, this indicates Knuckles' playthrough might take place after Sonic's. There are a few other tidbits in the game which indicate this to be the case, as we see below. In Sandopolis Zone Act 2, the Hyudoro ghosts are accidentally freed from an Egg Capsule during Sonic's playthrough; when Knuckles gets to the same point, the pod is already cracked open. Combine this with the Death Egg's absence in the roof of either Lava Reef or Hidden Palace Zone, and it seems that Knuckles' playthrough must occur at least after the battlestation launched (witnessed in Sonic's Sky Sanctuary Zone). More possible info from Sky Sanctuary includes when Sonic went through the zone, it was pretty much destroyed from Mecha Sonic's explosion. When Knuckles arrives... he is on the last surviving remnant of the ruins, which are promptly finished off by his battle with Super Mecha Sonic. This means they could NOT have happened at the same time, or else Knuckles would have a lot more level to travel.
If we infer from the points above that Knuckles' story takes place after Sonic's "middle" ending - where the hedgehog had the seven Chaos Emeralds in the Doomsday Zone, leading to the Eggrobo wreckage scene - then at the end of Sonic's story Knuckles got the Master Emerald back, and Angel Island began to rise out of the sea. Indeed, we see that the island is clearly up in the air during Knuckles' last boss, Super Mecha Sonic. Even in the Sonic 3 parts of Knuckles' playthrough there are signs that Sonic's Sonic & Knuckles story has concluded; the ocean background from Sonic' Angel Island Zone is replaced with sky when playing as Knuckles, and the crashed Death Egg is gone from the Launch Base Zone Act 1 backdrop. Lastly, in Knuckles's Mushroom Hill Act 1 the entrance to the corridor that Knuckles closes in Sonic's story is open, indicating that someone was inside.
Another difference is in Sonic's story, Sonic defeats Mecha Sonic, but the robot does not explode, he mearly looks shorted. Mecha later fights Knuckles, and after Knuckles beats him, THEN he explodes.
A small oddity might be the presence of the Flying Battery in Knuckles' playthrough (with Robotnik instead of Eggrobo as a boss, to confuse matters further), despite the fact that the airship was seemingly damaged or destroyed in Sonic's story. The game staff have indicated that Robotnik's presence here is simply due to the fact that there was no available sprite for Eggrobo in the Hang Mobile's cockpit.
A bug also sometimes sees Knuckles fight Robotnik in Mushroom Hill Zone.
It seems a reasonably safe conclusion, especially given the Lava Reef / Hidden Palace space station absences, that Knuckles' adventure occurs after Sonic and Tails have flown away from the island (although Sonic briefly returns with the Tornado to catch Knuckles in the ending).