Some spells cause other objects to deal damage, such as spells that have two creatures fight. In those cases, it's those other objects that are dealing damage, not the spell itself, and this will not cause Flame Channeler's abilities to trigger.

"A spell you control" means a spell on the stack. Usually, spells on the stack can deal damage only as part of their own resolution.

A spell that becomes a permanent and then deals damage, such as one that has a triggered ability when it enters the battlefield, will not cause Flame Channeler's abilities to trigger.