A couple of seconds?
To clarify, the Igla MANPAD system is modular, consisting for the purpose of this discussion a Launcher Control Assembly and the Launch Tube. The launch tube is a sealed unit with the missile contained in said tube. Once launched, the missile tube can be 'recycled', ie a new missile loaded and sealed in the tube and ready for next launch. This usually takes place at the base/supply depot but I see no reason why it cannot happen in-field in an operational situation.
Be that as it may, that's not what is strictly relevant here: I mentioned that the system is modular, ie at operational deployment you as MANPAD operator will have multiple launch tubes at your disposal, the number obviously dependant on operational parameters, supply-lines etc etc.
Subsequent to launch, the now-empty launch tube is detached from the Launcher Control Assembly. A new launch tube is taken and clipped into place on the Launcher Control Assembly and you're ready to fire again.
Rinse and Repeat.
As you can see, a couple of seconds is maybe a guess, but it's as quick as the #2 can get a new launch tube attached to the assembly and the time it takes for #1 to track.