The logo must play off the bird connotation of "fledge", as in the state of development where a baby bird is ready for it's first flight. Somehow keep the "baby" aspect to the bird, as a fledgling is about to take its first flight, not just any flight.
Like the Jaguar logo, I'm envisoning a strong sense of movement.
And like the Jaguar and other logos, I have a strong preference for simple line drawings. Varying line thicknesses are good, as are other line-drawing techniques such as cross-hatching.
Be creative on the choice of Font and placement of the name. "Fledge" is the key word, and "LLC" needs to be visible, but not prominent.
The two attached pictures are from the pitch deck, both sourced from Flickr. In both cases, note that I had a very difficult time finding any pictures of birds which look both young but ready for their first flight. It seems birds tend to either look helpless and hungry, or fully grown. Please avoid the helpless and hungry side of that spectrum.