In the Dragonlance novel Dawning of a New Age, a dragon kills another dragon and consumes the dead dragon's essence to become more powerful. Is this process supported mechanically in D&D 3.5e?
After dusting off my old Draconomicon to research this question, the literal answer appears to be no; there is no explicit process whereby D&D dragons can immediately gain power by ingesting the flesh of dead dragons. There are only three explicit means of gaining power for a dragon: age, which increases its draconic hit die; experience, which allows it to level in adventuring classes and/or Dragon-specific classes; and treasure or lore, which increase a dragon's standing in the draconic community.
However, there are both figurative mechanical means for this, and suggestive non-mechanical indicators there may be some benefit to it. In the Draconomicon section on diet,
[A dragon] converts its food into elemental energy and stores it for later use. Much of this stored energy is expended on breath weapons and on the numerous growth spurts that a dragon experiences throughout its life.
This suggests that food (in some capacity) supports or possibly even accelerates draconic aging, the primary method of gaining power. Although no mechanical system is provided, it would perhaps be reasonable to decide that eating another dragon (or some important part of the other dragon, such as its heart) might automatically age a dragon by a portion of the other dragon's lifespan, potentially increasing its HD and powers/size accordingly.
Figuratively, creatures may construct grafts from draconic organs and skin, as detailed in Races of the Dragon under "Draconic Grafts" (and excerpted here). Although the section as-written seems to imply humanoid grafters and graftees, it doesn't explicitly require such; presumably, a dragon could also benefit from a draconic graft.
Characters can level up using exp by defeating monsters. See p36 of the DMG.
When the party defeats monsters, you award the characters expe- rience points (XP). The more dangerous the monsters, compared 8th 25 dice to the party’s level, the more XP the characters earn.
Killing another monster is a way to level up, such as a dragon.
They can also get story awards. As p39 of the DMG notes
STORY AWARDS Such rewards should be fairly large
If eating dragon flesh is an important part of the story, as you imply it is, you could also award a lot of exp for that. I have in some games awarded story awards for PCs that eat monster flesh when eating monster flesh is lorewise a way to level up and they've enjoyed the culinary style to the game.
NPCs, notably can also earn exp. As p107 of the DMG notes.
PCs gain experience the same way PCs do. Not being adventurers, however, their opportunities are more limited.
In dnd 3,5 forgotten realm there is a red dragon named Klauth that eats other dragon eggs to increase power.
From Forgotten Realms Campaign Setting (p.168):
Klauth hunts for ands devours all dragon eggs and hatchlings—except for red dragon eggs, which he uses in a secret magical process to increase his size, health, and vigor.