Let's first think about what causes solar flares. The processes behind them are not substantially well-understood, but we do have some ideas. Magnetic reconnection is one possibility. Essentially, the magnetic field of the Sun quickly changes in shape and topology, releasing a substantial amount of energy. The result? A solar flare, a coronal mass ejection, or something similar. The same sort of process likely happens in flare stars.
So, if you want to trigger a solar flare, what do you have to do? Disrupt the Sun's magnetic field. The great bit about this strategy is that there isn't really long-lasting damage to the Sun, like there might be if you chucked another star at it (pro-tip: don't do this!). If you can, for instance, subject it to another really strong magnetic field, you just might be able to trigger reconnection.
Okay, but how can we do this? The ideal source of the magnetic field is . . .
- Not very massive, so you don't mess up the orbits of the planets.
- Stable, so it survives the encounter without triggering some catastrophic magnetic event.
- Fairly simple, if possible.
1. A magnetar
A close encounter with a magnetar could be a possibility. They're neutron stars with extremely high magnetic fields. Unfortunately, their masses are about two times that of the Sun, but if you're looking for some nice magnetic activity, a pass by a magnetar might be what you're looking for. Plus, you don't need to build anything; these are natural objects.
2. A gas giant
It has been hypothesized that hot Jupiters are responsible for superflares in some Sun-like stars. The theory is that the magnetic field of a gas giant orbiting close to the star becomes entangled with the star's magnetic field. Reconnection eventually happens, giving off a huge amount of energy; superflares can have energy 1,000 to 10,000 times that of a solar flare. Plus, they occur in Sun-like stars, and they can occur many times over large timescales.