@V10lentray
As DaveW stated, any bonuses added to one attack do not affect subsequent attacks. You can think of them as individual attacks always of 5 + 4 + 3 + 2 + 1 + 1 + ... dice which could be independently improved by bonuses but any bonuses would only affect the one attack being improved and not subsequent ones.
@DaveW
You make an interesting analogy, except that Burst of Thorns explicitly states that the Vines are also the ones making the attack, in addition to being the source of the attack. I shall grant you that the wording in the FAQ does make it sound like it is because the Vine Marker is the source of the attack that the attack doesn't benefit from the Traits of your Mage, and that is a very compelling argument. However, I still think it is because the Vine Marker is the attacker that prevents it from benefiting from the Traits.
With Chain Lightning it is very clear that the Mage is the attacker and the source for the first attack. The source then changes for each subsequent attack, but not necessarily the attacker, and the source is NEVER the spell itself like it is with Damage Barriers. Thus, either the spell benefits from the Traits of the Mage for each attack, or it benefits from the Traits of each individual source as it makes new attacks. I opt for the first interpretation as the second interpretation has weird consequences, but I can not say the second is completely invalid and you do present some compelling evidence for it. However, it most definitely does not work like a Damage Barrier and you can not say the attack is originating from the spell itself as the rules clearly say otherwise.