Interesting question. If they had floo powder, then I cannot see why not.
Muggles are likely able to use most magical artifacts that require no additional spellwork to use. They could ride brooms, for example, or use the floo network, if they had access to a broomstick, or access to floo powder and a magical fireplace that is thusly connected.
It isn't entirely unlikely that it has happened before in the past, and is one of the jobs of the Ministry to keep track of such events, so the artifacts can be confiscated, and the muggles' memories modified, and any witch or wizard responsible fined or imprisoned for various crimes of negligence.
Being able to perform such magic requires being a wizard or witch. The assumption that non-magic folk can do these things if they steal such objects was the premise by which Umbridge was imprioning muggleborns.
It may be possible for muggles aware of the wizarding world. Parents of muggle-borns, for one, need access to certain magical places such as Diagon Alley; while by no means neccesary, the option of floo travel would be a great convenience, especially for families who live far from London (as Hogwarts services all of Britain). I would imagine that parents of muggle-borns, as well as other non-magic folk like squibs or muggles that marry into a wizarding family, could use the floo network under certain conditions.