Worst I've ever seen was 8 seconds from idle to MTOP, which was on an Adour engine fitted to a Hawk T1. No significant experience of airliner engines, so can't help there although more modern fast jets tend to be shorter.
The term "Spin up" incidentally is actually used for the stress case in undercarriages when it first impacts the ground on landing. "Spool-up" is the correct term.
G