I found a way to get quickly past the fire at the start of level 14.

At the start of the level, you need to enter the crate and go right without stopping, and right before touching the fire you need to release a charged crate jump. If done right, the pirate will jump from the crate and at the same time will continue to the right with the fast pace of the crate. You will know it worked if you didn't die and also turned into dwarf pirate.

This probably works because how the game glitches when getting inside or outside crates at the same frame of getting into fire, which is a variation of what @Spoodsy said here: https://www.speedrun.com/post/fog85

Note that you need to do another charged jump during the fall in the right section, so you can turn back to normal size pirate and continue the level normally (dwarf pirate can't jump).

For this setup, I like to keep 2 fingers of my right hand pressed on the "down+right" arrow keys, and the finger of my left hand pressed on the "up" arrow key. You can prepare a charged crate jump during the transition between level 13 and 14 during full runs.

It can take a bit of time to practice and learn the exact position/timing of the trick, but it's way easier than the previous way I used to do level 14.

Here is a demonstration (I keep the up arrow pressed after the initial jump):