The first question is about what it means to “qualify” for an “option” since chameleon includes this blurb about aptitude focus:
You can’t use any abilities gained from your aptitude focus [...] feature abilities to qualify for a feat, prestige class, or other option.
The first question is whether or not a magic item is an “option” that you have to “qualify” for in order to use it. The word “qualify” is not used anywhere in the magic items section, and it is used for things like feats and prestige classes, which this section explicitly lists—but “other option” is impossibly broad and really quite vague. I do not think that activating a magic item is similar enough to qualifying for a feat or prestige class to support preventing magic-item activation on these grounds, however. The term “qualify” is used a lot when discussing feats and prestige classes, and the fact that it never is for magic items is important, I think. But ultimately this is only a circumstantial case, and a DM is going to have to rule on it.
Anyway, even assuming that that is no barrier, we still have to consider the actual activation rules:
Spell completion is actually a little more straightforward here: it requires that you be able to cast the spell. So any arcane spell whose caster level is not greater than the chameleon’s, the chameleon could use in scroll form.
Spell trigger is more complicated. The requirement there is that the item contain “a spell on your spell list.” The problem is that it’s unclear if the chameleon can even be said to have a spell list:
You gain the ability to prepare and cast arcane spells, which may be chosen from the spell list of any arcane spellcasting class.
That means either the chameleon has no spell list (it just poaches other lists), or it has a list that is the union of the spell lists of every arcane spellcasting class.
To answer which it is, consider the similarity to the wording for paladin:
Beginning at 4th level, a paladin gains the ability to cast a small number of divine spells, which are drawn from the paladin spell list.
Nothing else says that when you take levels in the paladin class, the paladin spell list becomes “your spell list,” and yet the spell-trigger rules call out paladins explicitly with “(This is the case even for a character who can’t actually cast spells, such as a 3rd-level paladin.)” To me, this means that a chameleon should be able to activate spell-trigger items as well. For that matter, spell-trigger activation is initially described as
similar to spell completion, but it’s even simpler.
If it’s simpler, the chameleon shouldn’t be able to use spell-completion items of spells he couldn’t use spell-trigger items of.
You do have to actually choose arcane focus, however, to have any feature at all that includes spellcasting. On days where you do not choose arcane focus, you have no spell list and cannot use these items.