The only non-Wilderness location to kill red dragons is Brimhaven Dungeon. Access it using either the Karamja lodestone, a brimhaven tablet, the boat from Ardougne, or an amulet of glory. Entrance to the dungeon costs 875 coins, unless you've completed the Hard Karamja Tasks. Inside the dungeon, chop the vines, and if you've completed the elite tasks and are wearing karamja gloves 4, use the agility shortcut directly south from there to take you to the red dragon area. Otherwise, take the long path south and use that agility shortcut to enter the area. See Map:Brimhaven Dungeon for more information.
Red dragons are weak to crossbow bolts, but with high level weapons you could use Magic or Melee as well. Super antifires are strongly recommended, as they will allow you to use both hands for weapons instead of an anti-dragon shield or equivalent. Using a Beast of Burden is also helpful to cut down on the number of bank runs. Simply attack the red dragons with abilities and pick up the hides and bones. With relatively high combat skills, you can kill them in about 10 to 13 seconds on average. When your inventory and your familiar are filled, teleport to a bank using a TokKul-Zo or ring of duelling, bank, and repeat. Using atleast a Sign of the porter II (level 28) will help to automatically bank the red dragonhide.At level 37 prayer, The Protect from Magic prayer can be used to replace the need for Antifire potions. This prayer provides the same immunity to chromatic dragon dragonfire as Super Antifire or Antifire Potions. It is therefore recommended to pray against magic instead of using other means of dragonfire protection for players who can kill the dragons quick enough to offset the cost of Antifire potions with Prayer Potions.