The phrase "be thick as flies" means to describe a situation where there are many people or things in one place, often in a crowded or chaotic manner. Some synonyms for this phrase include "be swarming," "be packed," "be teeming," "be crowded," or "be inundated." Each of these phrases includes the idea of many things or people being in one place at the same time, but each has a slightly different connotation. "Swarming" suggests an overwhelming amount of activity, while "teeming" implies a more controlled and organized situation. "Inundated" implies a feeling of being overwhelmed, while "packed" and "crowded" suggest a sense of physical closeness.