Storybird is now Flash-free and built entirely in HTML. With Flash, full-screen playback was easy. That's what Flash was built for. With HTML, full-screen is newer and much trickier. Some browsers support full-screen, some don't. Same with hardware; it varies.
This makes full-screen availability a touch-and-go proposition. You may have the right browser, but not the right hardware, and vice-versa. It's *very* hard for you to figure out and it's impossible for us to diagnose.
The only advice we can give you is: use the most recent browsers and hardware you can get; the chances of it working improve.
1. We continue to optimize full-screen controls as browser makers release new editions (which is frequently, particularly with Firefox).
2. We removed Flash to focus on open web standards and not invest in sluggish, proprietary plugins. Not only was Flash a memory hog that compressed images and typography, it made it near-impossible to make our editor multi-lingual and, rather famously, does not work on iOS.