If you decide to go the rappel route that others have suggested (that would be my suggesstion too!), you really don't need to buy yourself a nice harness. You're trying to escape from a burning building, not go on a climbing expedition. Some flat webbing made into a "diaper sling" would work just fine. Get yourself a locking carabiner (or two regulars - oppose the gates), a figure 8, and some climbing rope and you're all set. By "climbing rope" I don't necessary mean top dollar kernmantle stuff. We used to use what was called "Goldline" for rappelling. Not very good for climbing (too stretchy and stiff) except maybe for top-roping, but OK for rappelling. Find yourself an old piece of retired firehose (ask at a fire station) and cut off a 5 foot piece of it. Use it as a protective sleeve over your rope where you hand it out the window over potentially rope-cutting clutter.

Or, just take the stairs if you can!