There were some exceptions in the 1940s and 1950s, when jet engines didn't quite have enough power to get aircraft up to flying speed quickly. There were some attempts to use rocket-assisted takeoffs ("RATO" or "JATO") during WWII, and by the 1950s, this worked reasonably well. This peaked with the B-47 bomber, which was basically a jet fighter scaled up to heavy bomber size. Here's a JATO-assisted B-47 takeoff.[1] And here's a jet fighter zero-length takeoff from a rack on the back of a truck.[2] That was pushing it; there were a lot of crashes.
Awesome, but impractical, the technology was discarded in favor of aircraft with enough main engine power to get off the ground on short runways.
Another dead end was the Avro-Car, which was supposed to be a VTOL for the Army. This is the famous flying saucer.[3] It was supposed to be a supersonic VTOL. It had nowhere near enough power for that, and could barely get out of its own ground effect. Plus it was unstable, although today it could probably be stabilized automatically. The prototype finally ended up at what's now NASA Ames, bouncing around the back lots in hovercraft mode. The U.S. Army was also funding the UH-1 helicopter, which was less awesome, but far more useful, so they cancelled the Avro-Car and ordered lots of Hueys.
If you like weird VTOL craft and are in Silicon Valley, visit the Hiller Aviation Museum. Many of those strange ideas from the 1950s ended up there.
So, using a booster to get a large ornithopter off the ground is, while not impossible, probably not something you'd do often. Although you could imagine some fortress having such a rig, so the leaders could escape when they were losing.
[1] https://www.youtube.com/watch?v=vKQYG_fA2uM