The red dragonflight didn't even notice the first war, and probably wouldn't have noticed the second either, if not for Deathwing. The crafty old aspect of earth had managed to pierce the magics that kept him from finding the Demon Soul, and while he couldn't use it himself, he could lead others to it: soon the red dragonflight, even the dragonqueen herself and her ancient mate Tyrannastrasz were under the control of filthy little mortals from another world, the orcs of the Dragonmaw clan.
This humiliating period of captivity lasted eight years, while the Dragonmaw at Grim Batol kept hold of the Demon Soul. During that time the aspect of life was forced to breed constantly in order that the orcs might use her children as living weapons against the other mortal races. To put this into perspective, aliens from another world who'd sold their very souls to demons by drinking their foul and tainted blood repeatedly used a magical artifact to rape both the dragonqueen and her elder consort by proxy and then took the resulting children of the greatest protector of life imaginable and hurled them, barely out of the egg, into combat that saw them slaughtered at a time when all the dragonflights (including the red) were in decline and every hatchling was precious. This forced breeding so weakened Tyrannastrasz (not to mention that he was actually older than his queen, and not blessed with the power of the Titans to compensate) that in the end he chose death fighting Deathwing over the possibility that it might continue.
Eventually, a ragtag band of misfits including that time traveling red dragon and human mage, a high elf ranger and an extremely crazy dwarf helped destroy the Demon Soul and restored the power lost to it to the four aspects who had been tricked into helping with its creation, including Alexstrasza. So restored, the four aspects fought Deathwing (and were kicking his scaly, crackling, lava seeping keister when he bravely ran away) and Alexstrasza used her restored powers to help create new blue dragons to revitalize the blue flight to some degree. (Perhaps she couldn't have managed it before the Demon Soul's destruction, and also possibly enduring her own offspring's dire fate at the hands of the orcs moved her.) The dragons also assumed control of Grim Batol, the site of their eight year ordeal, perhaps to guard it against intrusion or possibly simply out of a desire to keep their shame to themselves.
Following the second war the red dragons were curiously absent from the third, although they may well have simply been too demoralized and damaged by their experiences to truly take part. They did station guardians at the battlefield following the destruction of the World Tree, and did not give Fandral Staghelm
their blessing for the second world tree Teldrassil. They did, however, send an agent to oppose the work of Nefarian at Blackrock Mountain, the red dragon Vaelestrasz, who unfortunately fell victim to Nefarian and had to be put down by mortal adventurers on their way to kill the black dragon. They were forced to abandon Grim Batol but recently due to events in the novel Night of the Dragon
and have not yet returned (and it seems unlikely they will find time to do so). The upcoming raid instance the Ruby Sanctum
will expand on what the red dragonflight's current concerns are.
Since then, red dragons have been most notable in their efforts to oppose the blue dragonflight and Malygos in Northrend as the aspect of magic sought to utterly cut off the mortal races from the magical power flowing through the world's ley lines. While an argument could certainly be made that the mortal races are often dangerously incapable of controlling the magic they unleash and that Malygos might have finally been doing what he should have done at the Well of Eternity ten thousand years earlier, in the end his reckless alterations to the world's magic caused as much damage as it would have prevented, and the red dragonflight was forced to oppose him. His death came at the hands of a group of mortals assisted by a host of red drakes.
Currently the red dragons are led by Alexstrasza and her surviving consort Korialstasz. There's not much hierarchy aside from this: red dragons such as Caelestrasz or Vaelestrasz are, after all, the children of Alexstrasza and revere her both as mother and leader. It is unclear if the dragon aspects are in fact truly siblings or if they simply refer to themselves as such due to their position as being directly empowered by the Titans themselves, but with the revelation of Galakrond as the progenitor of all dragonkind, it's certainly possible.