Let's see
Shadow enhancement to armor - competence
Ring of Chameleon - also competence
Cloak of Elvenkind - competence again
Subtle Slippers - competence, I'm seeing a pattern here.
Ring of Shadow - unable to locate but ...
Sniping weapon enhancement - competenceSo outside of maybe the Ring of Shadow being some other kind of bonus no the highest competence bonus present would be what you've got.
And while circumstance bonuses can stack they do have to be due to differing circumstances (IIRC) so its largely a GM call there.
With this set, you only get the best one.
/cevah
"Bonus: Bonuses are numerical values that are added to checks and statistical scores. Most bonuses have a type, and as a general rule, bonuses of the same type are not cumulative (do not “stack”)—only the greater bonus granted applies"
"Bonus Types: (...) The important aspect of bonus types is that two bonuses of the same type don’t generally stack. With the exception of dodge bonuses, most circumstance bonuses, and racial bonuses, only the better bonus of a given type works (...). The same principle applies to penalties—a character taking two or more penalties of the same type applies only the worst one, although most penalties have no type and thus always stack. Bonuses without a type always stack, unless they are from the same source."
Spell requirements are spell requirements and generally have nothing to do with the effects of the item other than thematic appropriateness.
A competence bonus generally makes you better at performing some task, usually temporarily and in a manner that doesn't lend itself to other bonus types. In this case, being able to change your colors to blend into your surroundings makes you better at hiding and sneaking.
Competence bonuses are very common for skill checks and ability checks. Paizo could have made the item give an enhancement bonus instead, but skill checks usually don't get enhancement bonuses. They could have made it untyped, but they probably didn't want it to stack with other similar bonuses.