I have recently decided to run Rappan Athuk - Dungeon of Graves again, and due to the difficulty of the dungeon, I have decided to allow Gestalt Characters. One player applied with a Warlock/Dragonfire Adept, and he is going to try to talk his way through the campaign. He got an 18 on Charisma (we start at Level 4), and gave himself 7 ranks on Diplomacy, Intimidate and Bluff each. He then took the Beguiling Influence invocation as one of his Warlock invocations, then took the same again for one of his Draconfire Adept invocations. Now this invocation gives him +6 on each of those skills. +13 bonus is already very good at level 4, but he reckons he can cast both invocations at the same time, as it is (in his mind) different invocations belonging to different classes, giving him a total of +19 bonus at Level 4 already. Is that legal?
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This is known as the same-source restriction. Since both bonuses are coming from the same invocation (beguiling influence), they do not stack. It is not two separate invocations just because both classes grant access to it. Even in cases where there are differences (say, a cleric and a wizard both casting the same spell on a fighter, once arcane and then divine), it would still be the same spell and not stack.
I see your player's line of reasoning, tortured though it is. Bonuses of the same type don't stack (except circumstance bonuses, and even those don't if they arise from the same circumstance). But untyped bonuses do stack, and beguiling influence's bonus doesn't have a type listed. I don't know why they didn't make it a competence bonus, but they didn't: both books agree that it is untyped.
However, the same spell does not ordinarily stack with itself, even if it's cast from different spell lists, and the same goes for spell-like abilities. Haste is the classic example here, to the point where the SRD even states it explicitly in the spell description. Beguiling influence doesn't say that it stacks with itself, and both books also agree on this. They had a chance to amend the description in the second book, if they'd intended it to be usable the way your character describes. They didn't.
(That said, be nice and let the player retcon a different invocation into one of his lists, so that he's not doubling up anymore. The character should have known that doubling up makes no sense).