It's man made.
The big 3 (China, Russia, and USA) have the capability of placing advanced landers on the moon for decades.
The big 3 also have fleets of satellites orbiting the Earth.
They can command these satellites to do more than just orbit. They can actually fly around and change their orbits and do "other" things.
They send commands by radio links. The problem with radio is that it can be intercepted and more importantly, can be easily jammed to make these satellites useless.
Instead, they now send commands via Infrared lasers from landers on the moon. Being light, they can not be jammed or interfered with since the photodetectors are pointed toward the moon and away from the Earth.
The light flashes being seen are used as aiming devices for the satellite. The visible flashes are a super fast pulse train, which they first send the address of the satellite then the final checksum.
The actual commands are sent via a 200 watt infrared laser (invisible to the naked eye) along with a checksum. Both checksums must match to be accepted as a valid command to the satellite.
...or it could just be aliens...