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If Water Pledge and Fire Pledge are used in the same turn, the ally moving second will use Water Pledge with a power of 150, and create a rainbow on the user's side of the field for four turns. The rainbow doubles the probability of secondary effects taking place for moves used by that side of the field (not including Secret Power)

It only doubles the secondary effects of moves used by the side that used Water Pledge and Fire Pledge. It also affects the chance of King's Rock.

Grants all attacking moves that do not already have a chance to flinch
a 10% chance of causing each target to flinch. This chance is affected
by Serene Grace and the rainbow created by Fire Pledge and Water
Pledge.

Source
Source 2

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https://bulbapedia.bulbagarden.net/wiki/King%27s_Rock says king's rock is affected by the rainbow.
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Yes, it does increase the chance of the effects of held items happening of the users by .50%.

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How do you know this?
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The Abilities Stench and Poison Touch and the held items Razor Fang and King's Rock grant additional effects to moves.

The rainbow doubles the probability of additional effects taking place for moves used by that side of the field (including the chance of flinching caused by King's Rock and Razor Fang)

Yes, all 3 are affected by the rainbow created from Water and Fire Pledge. Hope I helped!

Additional Effects Bulbapedia
Fire Pledge Bulbapedia

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The second source doesn't mention stench or poison touch.
The first one mentions it as an “additional effect”, and the second mentions “additional effects” that cause flinching are affected by the rainbow.
I wouldn't trust Bulbapedia that much. There were a few months when Bulbapedia said that adaptability boosts all STAB moves, so at the time you could have said that adaptability boosts moves of a Pokemon's previous type after it Terastallizes. Bulbapedia also didn't mention that teleport ignores trapping, so you could have said that trapping prevents teleport. If a question asks for the interaction between 2 game mechanics, I would trust Bulbapedia to answer it only if it explicitly tells me what the interaction is.