When can I react with Kharox trigger ability, after burn 3 or before burn 3?

You can react at both points — there are two separate reaction windows.

Before Burn 3: Once Kharox becomes Empowered, his "When I become Empowered" triggered ability goes on the Chain. At this point, players can play Reactions (e.g., remove Kharox or respond to the trigger). Note that killing Kharox in response won't stop the trigger — it's already on the Chain — but it can affect the reflexive trigger that follows.

Then the trigger resolves → opponent is chosen → they Burn 3.

After Burn 3: The "Then you may do this:" part is a reflexive trigger (Rule 387.1 — uses the exact phrase "Do this:"). Once Burn 3 finishes, that reflexive trigger goes on the Chain as a separate pending item, creating a new reaction window. Opponents can respond here too (e.g., by removing key cards from the opponent's trash before Kharox's controller gets to pick one).

Both windows are valid, but they target different moments — the first lets you respond before any burn happens, the second lets you respond after the trash is populated but before the unit is pulled from it.