I've ran a Ego SS based build some time back post-alert with Fire Strike and always noticed Clinging Flames' damage per tick always staying in the two-digit number range (wiki states that it's 27) so I'm very sure that Ego's ranged damage buff does not apply to Clinging Flames. Fiery Form will buff the damage since its type is fire.
offense will increase it as well as general dmg increase while in the hybrid stance, but it would be assumed that dot dmg unless specifically stated will not increase via ego stat
now if dot dmg is bugged and its supposed to be then gravy but for right now assume what has been said
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now if dot dmg is bugged and its supposed to be then gravy but for right now assume what has been said