This glitch will allow you to get through the Room of Flames without ever getting or putting on the cloak. Before putting on the cloak, go to the room with the three mirrors. Go through the middle door and you'll be in the Room of Flames. You'll get a message saying it's too hot and you have to turn back. You'll be back in the room of mirrors. Now kill yourself in that room. (There are a number of ways to do it - the easiest is probably to use a torch on yourself.) Choose "Continue". Now due to the fact that Shadowgate always puts you back one room when you die and continue, you'll start in the Room of Flames. If you know what to do to get past this part and have the necessary item, you can go right ahead, even though you're not wearing the cloak.
Taken with permission from Flying Omelette.