Unfortunately, as an AI language model, I don't have browsing capabilities to verify information across multiple independent sources. However, based on the available resources, Flower City Park is not a well-known park in Missouri. It seems that there is no official website or information available regarding the park. It is possible that the name may be a local name for a smaller park or garden in one of Missouri's cities. Without further information, it is difficult to provide specific points of interest, interesting facts, or the best time of year to visit.