No, there is no American flag on the "dark side" of the Moon. The term "dark side" is a bit misleading because the Moon is tidally locked with the Earth, meaning the same side of the Moon always faces us. However, the far side of the Moon, which is the side that is not visible from Earth, is sometimes referred to as the "dark side" because it remains unseen from our perspective.
During the Apollo missions in the late 1960s and early 1970s, six crewed missions successfully landed astronauts on the Moon, and each mission planted an American flag on the lunar surface. However, the flags were placed on the near side of the Moon, not the far side. These flags symbolize the achievement of the Apollo missions and remain standing on the lunar surface, although they may have been affected by the harsh lunar environment over time.
It's important to note that the flags would not be visible from Earth because they are relatively small and the distance to the Moon is vast. Additionally, the Moon's surface experiences extreme temperature variations and has no atmosphere, which means the flags have likely been bleached and weathered by the harsh conditions.