Living on a river delta is indeed precarious and the probable results of climate change would progressively add to the effect of wind and current as the sea level start to flood the delta, presently home to 100 million people, a mass migration into central Asia could trigger all sorts of events.

How long until this occurs?

According to ClimateHotMap.org it is only about 3mm per annum.

It depends on what melts. Sea ice does not matter so much but if Greenland were to lose its 2km icesheet, sea levels could cover much of this map.