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I tried it last night, only a couple times so not sure if something else may have effected it. But Solar Flare did make the DoT ticks do more dmg on the Sun Fire cast after it. For example on the same boss mob, cast Sun Fire was doing 57 a tick, waited for DoT to drop off, casted Solar Flare then Sun Fire and DoT was doing 79 a tick.
Both Sun Fire's and all ticks of its dot benefit from boosts like Dark Flare/ Solar Barrage and Might of the Guild. Volcanic Rune / Scalding Rune I think benefit only for the initial hit, but not sure - tested it long time ago.
during beta all "single use" spellpower/weapon damage bonus didn't apply to dot... that is because DoT and HoT are calculated every second and not at the moment of cast... so if your power increase or decrease after you cast a dot/hot the damage/healing will change in accordance...
I'haven't checked since release since I'm not using any "single use" boost like those... but as suggested it is quite easy to check ^^'