Solakar Flamewreath is spawned at the end of the "Father Flame" event in the Upper Blackrock Spire Rookery. The "Father Flame" event can be trouble for the unprepared and many groups choose to skip it. The event that spawns him begins by looting the pillar in the left side of the Rookery, surrounded by eggs and elite dragonkin.
The Rookery is full of whelp eggs that hatch if a player gets too close. While the whelps are easily defeated in smaller numbers, they can quickly overwhelm a group if not attended to promptly. Great care should be taken at all times to avoid hatching the eggs. Note that trying to clear the eggs beforehand is futile, as they have a fast respawn timer.
Begin by clearing out the few dragonspawn that occupy the Rookery as you enter. For this event the raid should be positioned as one large group inside the Rookery. This is to minimize LoS problems and to maximize the effectiveness of AoE attacks.
One character must activate the pillar in the far end of the room. It is practically impossible to approach the pillar without going near a few eggs and they will hatch. You can either kill these whelps or use a character capable of stealth. Even though stealth won't prevent the eggs from hatching, the stealthed character won't get aggro from the hatched whelps and after a short while they will despawn.
When the room is clear and the group positioned, the character at the pillar can loot it and start the event proper. The event spawns five waves of 2 dragonkin mobs ending with Solakar Flamewreath. The waves of dragonkin are combinations of Rookery Guardians and Rookery Hatchers. It is very important that all DPS is focused on the Rookery Hatchers as soon as possible. The hatchers move from egg to egg hatching them and adding whelps to the battle. The sooner they are killed the easier the encounter.
Solakar Flamewreath himself is a straightforward encounter and is relatively easy.