To be clear and flesh it out, "launched into a roll" is not an idiom. "Launched" by itself is somewhat of one. The roll is just a roll.
When we say "launch" we think of a rocket's explosive force quickly blasting off whatever it is. Or maybe a catapult. A salesman might launch into her speech about what a good product this is -- they started talking right away, not giving you a chance to say anything. A cat might launch itself off the dresser and into your lap -- that's faster and further than if they jumped.
Confusingly, we also use "launch" for new ideas, or commercial products, or store openings, but are thinking of a boat. We're "putting it in the water" for the first time to see if it floats or sinks. From context we can usually tell if launch means a rocket or a boat. We could launch into construction (start immediately) to launch (open) a store in December.
Another way to write that phrase would have been: "She quickly dove forward, tucking herself into a ball as she hit the floor, and smoothly turned it into a forward roll. That made her very difficult to shoot at and also, even though it makes no sense, was faster than running".