What if Kineticists got the option to voluntarily increase their Drained condition by 1 until their next daily prep as part of the action to Gather Energy, and then got to add their CON mod to damage to their basic blasts as long as they have that element gathered? Also, while they have that element gathered, add CON mod/d6 damage to your next Overflow action, kind of like how swashbuckler's Panache works - Overflow actions would be the analogue to Finishers, and the CON mod to damage on the basic blasts would work like the swashbuckler's precision damage with Panache.
This would give kineticists a mechanic that makes a high CON important, would give the opportunity for big burst damage limited by the kineticist's health, and would give them the ability to add CON to damage while actually capitalizing off of having 18 CON at level 1. Essentially, this is a way to implement Burn while keeping the mechanic simple enough for new players to understand, while keeping in line with existing design precedent.