How to compute the maximum power I can get from an optical fiber?
You have not provided nearly enough information, but let's start anyways. 

First, what wavelength? Second, how do you propose to couple the light to fiber? A fiber with a 1 mm core diameter is a pretty big fiber, but a 1 mm spot on the end of the fiber is a pretty small spot.

With that said, Thorlabs will happily sell you a 2-meter patch cord which will handle about 50 watts. And here's a company which makes cables which handle kilowatts. Laser cutters normally use fiber optic cables to transfer IR from the laser to the moving cutter head, so 10's of kilowatts should be available. That is not to say cheap, just available.