I need to pass along two pieces of advice for similar situations, while I pray that no one who reads this will ever be in a similar situation. I'm not going to go through all the safety tips because every family needs to go through that information in their own home and community, but I want to repeat two tips that I don't see shared often enough.
If you have to go through fire, first go into your bathroom or kitchen (whichever you can get to) and soak towels or any fabric (clothes, sheets, blankets) that you can grab on the spot in water and wrap it around you first. It makes an ENORMOUS difference to your survivability. The extra few seconds that it takes to soak a towel or two and wrap it around yourself or your children can make all of the difference. It not only keeps the fire off your skin for a few precious seconds but if over your mouth and nose it helps with the breathing too. So if you have a child, baby, or pet to carry and you absolutely must go through fire, wrap the child, baby or pet in one soaked towel and then a larger one around you like a cape that goes all the way around (a sheet doubled over is ideal, though a towel is thicker and great for head, shoulders and chest.) This was taught by fire departments when I was a child and I know it works.
The second suggestion is to take a chance with jumping rather than going through incendiary level flames. Broken bones can be fixed easier than third degree burns, especially over most of the body. Jumps from the third floor are survivable. Here is advice I learned again from fire departments back in the 1950's when folks in the country like our family often had to make our own rescues. Open the largest window that you have in the safest room. If you can squeeze a twin size mattress or futon out of the window, throw that out first. That will be your landing pad and also show you where you will land when you and your children jump. Be calling for help of course so passersby might hear where you are and come to help (there were several spectacular examples of heroism of this sort in NYC recently). But throw out the window all the "soft landing" material you can find: mattress, futon, pillows, cushions, even armloads of clothes, stuffed animals... anything you can quickly get out of the window. If you are by yourself climb out the window and get yourself in the position that you are dangling from the window sill by your hands, facing the building. This gives you a four foot advantage in the fall, If you jump from the windowsill level that is higher than letting yourself drop from your own weight with your hands holding onto the windowsill and your feet obviously dangling (depending on your height) below. Also it is less scary if you are facing the building and not looking down. It's like climbing a ladder, don't look down. If you are like me you can't hang on for long so let your body relax like jelly and let go and you will fall on the material you have thrown down before you. Don't try to land on your feet because that makes your body rigid. Let yourself be as limp as possible. When you let go if you can manage it wrap your arms around your head and neck. If you come down like a relaxed ball, protecting your head, you are more likely to roll than to break.
If you have children or pets, you have to throw them onto the soft material you have previously thrown out to break everyone's fall. If you have several children send the oldest or strongest down first because if they are uninjured they can help catch their siblings or pets. Again, as I gave advice about dropping from the sill rather than jumping, help the child out the window by holding onto their arms so they face the building and drop feet first as limply as possible onto the cushioning. If you have a sheet you can let a small child into it like a hammock and pass them down as far as you can reach. If you are reaching down with a child in a gathered sheet this lessens the distance of fall and protects their limbs. Put them in the sheet center and bring all four corners to the center, like a sack. Then lower them to rescuers, though if you are on the third floor of course you will have to let go. These few feet of difference and the cushioning can make all the difference. When everyone small is out then you should get out, as instructed above.
It is important to think through in advance, "what would I do if I was here or there in the house/apartment and fire broke out?" When I had a house I had a fire extinguisher in every room, not to fight the fire but to clear my way in front as I escaped. I thought it through and placed them accordingly.
I also thought through window escapes as I described above. One thing I would have done is to tie several sheets together and then push the bed to the window (or other heavy piece of furniture), tie the sheet end to the leg of the bed, and throw the tied sheets out the window to climb down. It's not just a "prison escape" joke but a real way to escape second and third floor fires.
I hope you never need this advice but here it is and be sure to include it in your general fire safety and escape preparations and procedures for your family. God bless all fire victims and the brave men and women of the fire departments who risk their lives every time they help others.