Where is the rule that the claw attack does its damage on a successful Vampiric Touch melee touch attack?
There isn't one- what you're asking of me isn't what I'm stating.
Everyone knows that a spell touch attack can occur on other attacks, but where is the rule that a claw natural attack occurs on a successful melee touch attack for Vampiric Touch?
Again, that isn't what I'm stating.
The additional wrinkle to the touch attack, here, a held Vampiric Touch spell, resolves independently of the underlying nature of the attack. The touch attack, regardless of its characteristics- a mere touch, a stunning fist, a grapple, a trip, a claw...no damage, some damage- its all immaterial to the effect of the VT spell. That spell will trigger even if the attack in question cannot do damage, such as on a bull rush. It pays no attention to the underlying nature of the attack, only whether the condition of physical contact has been met.
Likewise, the enchantment on the weapon "pays no attention to" the particular kind of attack made by the weapon- trip, strike, disarm- beyond whether "a successful hit" has been made. Trip, strike or whatever are all immaterial to the triggering of the enchantment's damage.
If I'm holding the charge on a Shocking Grasp, and someone punches, grapples, or trips me, do you consider that person to immediately become the target of the spell?
That's what the rules would seem to indicate, don't they?
My flail has rules that say it deals 1d8 damage "on a successful hit", too... and it doesn't mention caring if it's a standard attack or a trip.
Again with this?
Unlike the enchantment, the weapon itself is subject to the rules of the special attack as a subset of the normal combat/weapons rules. Its a physical limitation on the weapon and the way it is used in the delivery of the trip. Trips as a special attack don't deliver weapon damage, but some do.
Weapon enchantments, like other magic rules, are a seperate rules section. Like a held touch spell, they have their own triggering rules, independent of the normal combat/weapon rules.
If you want to play with weapons doubling up their damage on special attacks, that's your business as a DM.