ANIMAL WELL

Story-related; cannot be missed.

The P Flame is located in the northwestern quadrant. To reach it, you'll first want to get the bubble wand, slinky, and yo-yo from the three other quadrants. Lastly, you will get the disc in the northwest. To do so, ignore the dog head holding the disc in its mouth. Walk past it and continue through the linear rooms to eventually reach the mock disc. You can take the mock disc to the dog head with the real disc to swap them and get the real one. 

Now with all four items, you need to progress up and then to the right. You'll reach a room with two giant dog statues facing the center, with a shrine for the mock disc in the center. Once you've reached this room with the shrine, mark it on your map. What you need to do is return to the dog head where you stuck the mock disc and take it back, then bring it up to the mock disc shrine and place it there. The problem is that as soon as you take the mock disc, the dog boss will chase you relentlessly. Thankfully, if he gets you he only does one heart of damage rather than an instakill, but it's still stressful. Once you get to the shrine, insert the mock disc to get rid of the dog boss and open the door to the right, leading to this flame. 

As a side note, you can make getting back to the mock disc shrine with the mock disc much faster and easier if you collect at least eight secret eggs to unlock the animal flute, and use that to unlock the fast travel hub, and then activate the fast travel point in the northwest corner room, putting you only around four rooms away from the shrine.