How much time will it take pro app developer to create app like youtube?

To arrive at the precise time for developing an app like YouTube or Facebook is not that simple as everything depends on number of parameters like features, team strength, team experience etc. 

Let us consider some points that will directly affect the time it will take for developing an app like YouTube or Facebook.

1.      Features 

2.      Team Strength

3.      Team Experience 

4.      Finance Availability

You can refer the Blog How to build an app like YouTube – Cost, Features, Business Model for further detail.