I use Éric Cressey and Mike Robertson mobility routines (and SMR) and I feel it helps with overall flexibility and ROM. I do this before lifting.
For gymnastica exercices though I use one of Scott Sonnon's six minute warmup, and if I have the time or will, one of his cool down six minute routines.
On recovery days (again, time and will) I do a yoga or prasara light session.
What do you do yourself for your gymnastic routines?