Discarding 1 Spell Card is a cost to activate this effect.
If you activate the effect of “Chiron the Mage”, then flip it face-down, then flip it face-up all in the same turn, you can activate its effect again.
The restriction that you can only activate this effect once per turn is a condition, not an effect. So if “Skill Drain” is on the field, you can pay the cost once per turn (for no effect), but not pay the cost continuously in the same turn.