Time period depends, there is no set standard. Traditionally at all NCOES it is 5-7 minutes for warm up and cool down. Normally during unit PT it's a little longer, but in my opinion should never exceed 10 minutes. That will give everyone a longer period during the conditioning phase. It also depends on intensity of work out, more intense more time for recovery, low density less of a recovery period...IT'S ALL METT-TC!
I went through WLC a few months back and the cool-down lasted 5-7 minutes. Cool-down walk was until BPM was achieved. Each cool-down stretch was for a minimum of fifteen seconds (fifteen seconds each limb or per stretch). I do two or three stretching exercises, then do a self-stretch for 1-2 minutes, then dismiss.
Each soldier is different and will need to stretch alittle differently. Try looking into TC 3-22.20, carries alot of useful info and newest updated was as of March, 2010