Is there a formula to calculate power generated in a linear generator?

If we start off with the standard electric power calculation :

Watts = Volts x Amps

So you need have the voltage and the current to calculate the power generated. As this voltage and current, as originally figured out by Michael Faraday is the effect of a conductor, the coils in your machine, interacting with the magnetic field produced by the magnet you are using, you are well short of calculating any possible value for power generated from the information you have.

This basic electric power calculation formula is the sort of thing one usually is introduced to a student as part of a science - physics type of course at a secondary college level, if not as part of the syllabus common to most engineering courses in the first year or so. As you list an Engineering degree in your GrabCad profile I would have thought you would have been able to work this out for yourself.

To progress further towards calculating a value of power for the linear generator you are looking at there is no "simple no effort formula" you can blindly apply to get the answer you want. The voltage and current values that the linear generator you are looking into need to be determined before you can progress further. You need to read and understand a good text or two on inducing an EMF in a coil of wire, understand the factors, strength of magnetic field, distance between the field and the coil, speed that the magnetic field passes through the coil, just some of the factors that effect the power that you can generate. The value you have for the mass of the magnet, though, has one use, you can use this to calculate the force needed move the magnet through the coil ( F = Mass x acceleration)