Many people do have this.
It's called selaphobia. There's no real cause that can be pinned down definitively, but there are genetic and environmental factors that have been found to play a significant part.
Does anyone in your family have any anxiety disorders, or a specific phobia? If so, you may have a higher chance of developing this condition. It's just a genetic predisposition to developing psychological disorders.
If you ever had a negative experience with these flashing lights during childhood, then this could develop into selaphobia.
You may have actively avoided flashing lights to reduce your chances of feeling anxious, but doing so may worsen your symptoms long-term, as you're justifying your own fear. I think this is a real possibility here.
If it is really interfering with your daily life, then consider speaking to your GP about it. You may benefit from exposure therapy, CBT, or other options.