The flame room is pretty hard at first. I assume you most likely are having trouble with needing to jump into the area with the flame that constantly rises and falls inside it. The trick I used for that is to think of the flame in 4 stages: 1 stage rising 1 stage at the top and 2 stages safe to jump into. You need to time it so that you jump during the 2nd safe stage (right before it starts to rise) and, if all goes well, you should reach it when it is safe (you will still need to jump forward very fast though). The final jump looks bad but it's actually pretty easy.
