You need to register your EK account with Amex. This is pretty much instant during regular office hours. I think there must be some sort of manual check because doing it on a weekend or late at night means your status will go to 'pending'.

Once you've linked your EK account, the transfers are pretty much instant. There is a disclaimer that it can take up to 1 business day though.

PS: I see you're transferring gateway miles. Are you using an Amex Explorer credit card? The redemption rate on that plan is 4 gateway points = 3 skyward miles.