This post will explain how to use Kagetokage, and the basic mechanics of Trigger effects.
This is written with specifically April 2014 TCG Las Vegas Format in mind! Note that this ruling is completely different in the OCG, due to Trigger effects in Private Locations operating as Fast Effects (with "priority levels") in the OCG.
Let's first get some axioms out of the way.
Spell Speed dictates what cards can (or can't) be activated in a chain. You cannot chain a Spell Speed 1 effect to a Spell Speed 2 effect.
EG-1 : You cannot chain "Monster Reborn" to "Jar of Greed". This is because Monster Reborn (a Normal Spell) is SS1, and Jar of Greed (A Trap) is SS2.
EG - 2: You cannot chain the effect of "Elemental HERO Stratos" to "Trap Hole". This is because Stratos' effect (a Trigger Effect) is SS1, and Trap Hole (a Trap) is SS2.
When multiple Trigger Effects can activate at the same time, they must be activated in a particular order: 1. Turn player's mandatory effects 2. Turn player's optional effects
3. Opponent's mandatory effects 4. Opponent's optional effects.
EG-1: "Sangan" and "Dupe Frog" are destroyed by opponent's "Dark Hole". Sangan (mandatory) must be CL1. Dupe Frog (optional) must be CL2.
EG-1: Two "Mystic Tomato" destroy each other by battle. The turn player's Tomato must be CL1. The opponent's must be CL2.
The Kagetokage Ruling
Here is the common scenario which prompted me to write this: - Tin Goldfish is Normal Summoned. Its controller has "Kagetokage" and "Vorse Raider" in hand. - The opponent has an "Effect Veiler". The way this plays out is as follows:
The turn player's Trigger Effects activate on a chain. They can activate both Goldfish and Kagetokage, or either of those, or none.
Afterwards, "Effect Veiler" may be activated.
Let's say that they only used Tin Goldfish and that the Veiler was chained.
Kagetokage's effect cannot now be activated, as Trigger Effects are Spell Speed 1. A mechanically identical example is one that you have already read: You cannot chain the effect of "Elemental HERO Stratos" to "Trap Hole". You cannot chain the effect of "Kagetokate" to "Effect Veiler".
You cannot chain a Spell Speed 1 effect to a Spell Speed 2 effect.
When using 2+ trigger effects at the same time, you must declare all those effects at once. If you Normal Summon Red Gadget and ask, "effect?", it is not clear that you also wish to use the Kagetokage in your hand. You must declare both at the same time.