1
general::
Also, in no time at all;in less than no time;in nothing flat. Almost instantly, immediately, as in The train will be here in no time at all, or He'll be finished in less than no time, or I'll be there in nothing flat. All these hyperbolic terms equate a very short time with "at once." [First half of 1800s]
American Heritage Idioms
2
general::
Phrase(s): in no time (at all)
very quickly. (Compare this with in less than no time.) • I’ll be there in no time. • It won’t take long. I’ll be finished in no time at all.
McGrawhill's American Idioms And Phrasal Verbs