Ok, this is a bit complicated.
Bloodrager Kyton Bloodline gives this ability at level 8:
Now I know that armor bonus to AC does not stack with normal armor worn, just the highest applies.
But what if I went and wear a Haramaki to it, and enchant it with +3?
Obviously the +1 normal AC of the Haramaki doesn't count, but does the +3 enhancement bonus? AKA do I have 4 AC or 7 AC?
Your AC is +4, not +7. Armour bonuses of any kind never stack. The relevant rule:
The armor bonus from a suit of armor doesn't stack with other effects or items that grant an armor bonus
An enchanted armour has an enhancement bonus to its armour bonus - but the additional (+3 in your case) is still an armour bonus that doesn't stack with another kind of armour bonus.
You can stack non armour enhancements on the harakami (fortification etc) though - although this is open to interpretation and your GM may decide you cannot do so.
The Haramaki does NOT confer a +1 Armor bonus and a +3 enhancement bonus to AC to the character. The +3 enhancement bonus is to the ARMOR's armor bonus to AC. So then the character has a +4 Armor bonus from the Magic Haramaki, and a +4 armor bonus from the chains - which don't stack.
Are you sure the enhancement bonus is a "enhancement bonus to the armor bonus" and not an "enhancement bonus to the armor class" ?
The "armor bonus to armor class" might not stack with others, but that shouldn't mean the "enhancement bonus to armor class" doesn't stack with it, it's a different bonus.
I mean if it's actually a "enhancement bonus to armor bonus", then there's no question that it doesn't work, I just can't find that specified anywhere.
How about we bring up the relevant RAW before we outright dismiss his claim:
In general, magic armor protects the wearer to a greater extent than non-magical armor. Magic Armor bonuses are enhancement bonuses, never rise above +5, and stack with regular armor bonuses (and with shield and magic shield enhancement bonuses). All magic armor is also masterwork armor, reducing armor check penalties by 1.
In addition to an enhancement bonus, armor may have special abilities. Special abilities usually count as additional bonuses for determining the market value of an item, but do not improve AC. A suit of armor cannot have an effective bonus (enhancement plus special ability bonus equivalents, including those from character abilities and spells) higher than +10. A suit of armor with a special ability must also have at least a +1 enhancement bonus.
In truth, the book is abstract as to whether or not the enhancement bonus on a piece of armor is tied to the actual armor bonus, and since the bonuses are treated as separate entities (even if tied to the same item), they would be considered as such for the AC calculation. He could wear that Haramaki and get an effective +7 bonus to AC according to the RAW presented. (Or lack thereof.)
With that being said, I can guarantee you it goes against the RAI of Armor Enhancement Bonuses. Something to support that is the Bracers of Armor:
If a creature receives a larger armor bonus from another source, the bracers of armor cease functioning and do not grant their armor bonus or their armor special abilities. If the bracers of armor grant a larger armor bonus, the other source of armor ceases functioning.
Although Bracers of Armor is a wondrous item and doesn't exactly follow the rules of armor enhancing, it still presents that an item comprised entirely of an armor bonus (and maybe some special abilities), similar to any generic piece of armor like a Full Plate, would not stack with a piece of armor whose armor and enhancement bonuses would be either inferior or superior to those presented from the Bracers of Armor.
For further confirmation that the enhancement bonus of magical armor is applied to that armor's ARMOR bonus, look at any stat block of any monster or NPC wearing magical armor = the stat block will list only one single ARMOR bonus which will be whatever is appropriate for the armor type PLUS the armor enhancement.
For example:
Valkyrie (Bestiary 3):
AC 27, touch 19, flat-footed 24 (+8 armor, +6 deflection, +3 Dex)
Treasure triple (+2 breastplate, +2 returning spear, other treasure)
She wears a +2 breastplate which is AC 6 with a +2 enhancement modifier. That equals a +8 ARMOR bonus, which is exactly what is listed in her stat block.
Also, this is from the SRD but I don't have my books here to verify where this info came from:
Enhancement: An enhancement bonus represents an increase in the sturdiness and/or effectiveness of armor or natural armor, or the effectiveness of a weapon, or a general bonus to an ability score. Multiple enhancement bonuses on the same object (in the case of armor and weapons), creature (in the case of natural armor), or ability score do not stack. Only the highest enhancement bonus applies. Since enhancement bonuses to armor or natural armor effectively increase the armor or natural armor's bonus to AC, they don't apply against touch attacks.
If I take that bolded sentence and remove all the extra references to other things but leave the remaining text completely unchanged, it simply states: "enhancement bonuses to armor increase the armor bonus to AC."
It's important that you don't leave out the possessive. That 's is applied to both the armor and natural armor in that sentence, so the stripped down version should read:
enhancement bonuses to armor increase the armor's bonus to AC.
More important to me is the type of bonus. So what I care about is increasing the "armor bonus" moreso than the "armor's bonus". Even better would be to increase the "armor's armor bonus" but that is a) implicit and b) cherry picking (because the only place "armor's" is used is relative to "natural armor" and since I was excluding extraneous references it would be inappropriate to leave one in to cherry pick the sentence to match what I want it to say - especially since I don't need to cherry pick at all to demonstrate that it says the correct rule clearly enough on its own).
You're right everyone, I can see now it's clearly meant to work that way.
Sorry, this is a stupid thread, not sure why I even started it :(
Honestly, I'd see about asking your DM if you can enhance your built-in "Chain Shirt." I've heard people argue about magically enhancing the armor oracles get from some of their revelations (or at least using magic vestment on them), which are only hours/level; this seems to be permanent, so you'd have an even better case.