The answer should be “yes,” but unfortunately it’s not super well defined.
The first thing to realize is that on some level, people don’t really have caster level, or at least didn’t originally (straight back to D&D 3e). Instead, spells, and their effects, and magic items and their effects, have caster levels. What people have is the number that their spells and spell-like effects use for the spell/SLA’s caster levels, which is often referred to as “the caster’s” caster level but it’s not very consistent. Even the original item-creation feats include “caster level Xth” in their prerequisites, with no real explanation of what that means (it’s just understood to mean “when you cast spells, this is the caster level they have”).
The definition of caster level says “A spell’s power often depends on its caster level,” but then later says “In the event that a class feature or other special ability provides an adjustment to your caster level,” so even there isn’t super-clear about this.
So anyway, there are a lot of arguments on the Internet about whether kineticists “have a caster level” and so on, arguing that they rather have spell-like abilities, and it’s the spell-like abilities that have the caster levels. The problem with that argument is you can say exactly the same thing about spellcasters as well: they also lack anything saying that they have a caster level, they have rules that specify what the caster level of their spells is. That argument would effectively mean that no one can benefit from caster level bonuses, or take item-creation feats.
There is also an FAQ that says spell-like abilities’ caster levels don’t count for meeting item-creation feats’ prerequisites. That doesn’t really say anything about it working with caster level bonuses, but people extrapolate it to do so. The thing with this is most spell-like abilities have a fixed caster level, not a scaling one, and in some cases you can get a spell-like ability with a caster level higher than your actual level. So allowing those to work for prerequisites could be an “early entry” trick, which is why that FAQ was written that way (IIRC, it was reversing an earlier ruling on the subject). None of that applies to the kineticist, though, so there’s no “spirit of the law” reason to extrapolate from that ruling.
So yeah, the answer should be “yes.” I recommend that you rule “yes” if you are the GM, and if not, I recommend asking your GM to rule “yes” on these grounds.