Flying Blue transfers from Amex/Points.com (IME) and CapOne/Chase/Citi (from others' reports) tend to be instantaneous, though with any of the transfer/upgrade method pairings, there's a measure of speculation involved: the offered seat could evaporate before the miles appear.

Though if every mile you've ever earned with Flying Blue is from transferrable points, you may have bigger issues: it's not unheard of for AFKL to quietly cancel award tickets booked from accounts which have never earned an XP and lock the account. There are many datapoints of people showing up at the airport and not being able to reinstate the ticket, though nearly all of those are business class awards: Y and W don't seem to be a concern.