The phrase "imaginary flies" refers to bugs or insects that you think you see but aren't actually there. It describes seeing things that aren't real. Full definition
Some dogs snap at imaginary flies in the air or act as through they are chewing imaginary gum. (1800petmeds.com)
They studied 7 dogs who were presented for exhibiting snapping / jumping at imaginary flies using the protocol described above. (positively.com)
Interestingly, some dogs appear to watch and bite at imaginary flies in front of their faces — a behavior particularly prevalent among German Shepherds and Cavalier King Charles Spaniels. (positively.com)