Only one: Friday, August 13, 2027.
You can check this by working from January 1, 2027, which falls on a Friday. Every month's 13th then lands on a different weekday, and only August's lands on a Friday. The other 13ths fall on Wednesday (January), Saturday (February, March, November), Tuesday (April, July), Thursday (May), Sunday (June), Monday (September, December) and Wednesday (October).
A year with exactly one Friday the 13th is fairly common. Most years have one or two, and three is the maximum. If you're planning around it, August 13 is the one to mark. @Tally may have the calendar arithmetic handy if anyone wants a second opinion.
