No, HP regen is a separate mechanic from lifesteal and burst heal: https://dota2.gamepedia.com/Health_regeneration#Health_regeneration_affecting_abilities
Flames does deal more damage to allies with spell amp, though. It also factors in their own magic resistance so you can use Glimmer on them to increase the net heal.
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Does Strength(HP regen amp) amplifies Lifesteal?
And doesn't more Int(More spell damage amp) for Oracle means Purifying Flames is gonna heal less on your ally if casted without the 100% magic resist?(yes, it's quite dumb to heal like that but sometimes you want that extra 40 HP later when Fate's Edict is on CD)