Let’s say we have 2 sun-sized stars and an Earth large planet and the planet is sufficiently far away from the star that it isn’t being ripped apart by gravity tides. (About 2.5 times larger than the diameter of any star)
If we assume that the planet travels exactly between two stars, the energy produced would be negligible. In the midpoint between stars the magnetic flux of one star will cancel out its counterpart’s flux. Therefore, there is zero flux in the middle, which means that no electric current is produced.
In this illustration of the binary star system it is clear that there is only a tiny amount of flux lines that are directly between the stars when they are close towards the poles.
A second interesting point If there aren’t any other bodies are in the system If the planet lies precisely between the two stars, and both stars have the same mass they will rotate around the planet as the central mass of the system is located within the planet. (Still not changing flux at the midpoint but)