How do magnetic flux lines behave?

The general answer is "Predictably"! Magnetic lines are three-dimensional, surrounding a bar magnet on all sides.

Likepoles repel and unlike poles attract. When opposite poles of two magnets are brought together, the magnetic force lines join up and the two magnets pull together.

When like poles of two magnets are brought together, the magnetic force lines push away from each other and the two magnets repel each other.