Oomis, the pot is a kli rishon if it’s been on the fire (and still hot) no matter how many layers may be between the pot and the flame.
When the contents of the pot are poured into another vessel, that vessel is considered a kli sheini.
When the contents of the kli sheini are then poured into another container, that container is a kli shlishi.
Example: you have water in a kettle, on a flame or blech (or two, or three…). It’s a kli rishon. If you pour water from the kettle into a mug, that mug is a kli sheini. If you pour water from the mug into a cup, the cup is a kli shlishi.