Buffs do affect them, but noticing them can be a bit hard given the 5% variance on damage.

An individual kamihime's burst is basically normal attack damage times some multiplier* (plus a small constant tacked on at the end that isn't all that relevant). So buffs would directly affect this.
Burst streak damage is basically the sum of burst damage dealt that turn multipled by a percentage**, with elemental advantage/disadvantage adjustment***. There are also eidolons whose passive includes providing a bonus to burst streaks specifically, but in practice, you'd prefer to use some other eidoon.

*varies depending on the rarity of the kamihime, or main weapon for your soul. Also, the note you see for 3* kamihime or weapons saying increased burst damage, it's referring to a bump to this multiplier
**varies depending on the number of characters that performed a burst that turn. It's {1/(7-N)}
*** generally speaking, advantage means multiply by 1.45, disadvantage means multiply by 75%.