How long can your knight hold its breath and how much fire damage are you doing per round? I think you may run out of air first. Definitely an interesting idea if it’s already hurt.

5E characters can actually hold their breath for a silly amount of time, there's a solid chance here.

Assuming the knight has a +4 Con mod, they've got 5 minutes or 50 rounds before they suffocate. Heat metal averages 7 damage per round without upcasting, so you can expect around 350 damage before you pass out. A kraken has 150 hp on average, so it's done for

Amusingly, the rules do not technically specify a condition for the kraken to voluntarily regurgitate something, only for it to do so when triggered by taking a lot of damage in one go. Obviously no sensible GM is going to say that it can't do that, but by the most miserable RAW-only approach this plan actually seems to work

Now imagining a Kraken desperately trying to throw-up an Eldritch Knight while the Knight is trying as hard as possible to stay inside the Kraken.

BRB, writing to Ask a DM to ask about the propulsive force of a Kraken’s gag reflex…