I tried to use a leather jacket once. I also tried the leather from a leather sofa. Both were an acceptable thicknrss. The jacket was better than the sofa but neither was stretchy enough; i think they were just too old.
I recycle almost everything and i applaud any effort to reuse the old rather than but the new. But in this case, in my opinion,you need new. Use the old jacket and or sofa for handlebar tape, it's perfect for that. But get something new and stretchy for the saddle.