If you were going to have a group of six characters fight an adult red dragon, what levels would you want the characters to be?

CR 17 by the Monster Manual.

CR 17 means it is a good challenge for a party of 4 lvl 17 characters. So with six? Depending on the mix of classes, I'd go with lvls 14+ for a good fight. Also depends on location. Dragon in the open, where it can just fly up and strafe with breath weapons is bad, especially if the party only has one offensive caster, and not much in the way of ranged attacks. In a cave, there's less room to maneuver, but the dragon is stuck within melee range of the fighters. At level 14-18 there's still a risk of TPK, or at least a couple PCs getting eaten, but if done well, it will be one helluva fight.

If the dragon is in the open, then I will sat, if done properly, it will be a TPK.  However, even in the cave, the party will have its hands full as you can be guaranteed the dragon is not going to choose a home that will confine it.  It might not be able to fly, but it still as an arsenal at its disposal, not counting its breath weapon.  It has 2 claw attacks, a raking attack with its rear legs, a tail bash, wing buffet, in a cave can be quite deadly for a party.  Then it has its bite attack and last but not least, it has spells.  If the party is not properly prepared, it will be a TPK.  But even if the party is prepared, better bring a resurrection spell or two.  If there is anything left to resurrect.

as Tulgurth Suggests, it can really depend on how a GM runs them and the terrain/Preparation the group plays with.

A Cr17 creature Might be more or less of a Challenge dependent on these factors.

For me... Dragons are Seriously dangerous and generally not to me messed with.

bring body bags.

The timing of the fight is also important. Is this going to be the first or only fight of the day? Or is the dragon at the end of a dungeon the players have to fight through to get there? Do they have time to prepare, or are they going in blind? If you want to give your players an awesome fight, in their strike zone, but with a real chance they could lose if things turn south, after fighting through the dungeon to get to the lair, make it lvl 16-18, even with six players.

and your friendly gold dragon.

Red Dragons (or really any dragon with access to magic) in DnD is comparative to the Comic Book scenario of Batman and Spider Man.  Each with the right amount of time to prepare is and should be unbeatable.

Dragons are meant to be one of the penultimates of the physical realm in most fantasy genres.  As such, if they take the right amount of time to prepare, they should have so many magical protections, minions, traps, and the like in place; that they should be able to destroy any equivalent party that attempts to fight it.

An idea: it may be more fun (and more plausible) that there is some sort of 'weakness' associated to the particular dragon.  Give it a name, a lore, and a history.  Just a suggestion.

Great ideas and help.

What I'm actually contemplating is something of a cut-away flashback scene where the current players temporarily take the role of a heroic band that in days long ago actually fought the dragon and killed it.

The cinematic equivalent would be the scenes in Lord of the Rings/The Hobbit where we go back and see the battles of old actually happening. Here, instead of just describing it, the players would actually get pre-gen characters and fight it out.

The dragon winning would be problematic, but I have a plan for that.

(Any players in my game who read this thread -- pretend you did not see this :))