Could the sun be used as a way to facilitate time travel? Let's take a look at TV Shows and Movies that have done this before looking at weather it would be possible.
Some Movies and TV Shows that have used the sun to facilitate time travel.
In Star Trek IV: The Voyage Home kirk slingshots the Klingon Bird of Prey around the sun and takes the crew back in time to 1986 to find some humpback whales to take back to their time and save Earth from the oncoming probe.
This technique is used again in in Star Trek: First Contact when the Enterprise is brought back to its own time after fixing the time-line.
In Stargate SG-1's Season 2 episode 1969 the team are transported back in time when a solar flare interacts with the wormhole they are traveling through.
Now for the Science
In 1919 an experiment took place during a solar eclipse to see if Einsteins theory that the suns mass curves light. The results from the eclipse were compared with results from an experiment 6 months prior. The results of this experiment proved Einstein was right. This bending of light means that the light from the stars we see during a solar eclipse takes just over 1 second longer to reach us than the light from the closest stars we see at night. This is not much of a difference but it is a good place to start.
The slingshot effect, also known as the light-speed breakaway factor would require a space ship to travel at what Star Trek call warp speed towards a star. The ship starts to travel back in time is it approaches the star. Then breaking free, the ship is sent forward or back in time. This method would require very precise measurements to get you to your desired location in time, if it were possible at all.
First, you need a stable wormhole, this is simple in the Stargate universe but not so simple in reality as we have no proof they exist, and even if they did they would probably be to unstable to allow you to travel through. Then you need to time your journey just right to coinside with a solar flare, again we cannot do this at the moment.
So Time Travel is still Science Fiction