Any time the patient can cough or sneeze into the room – the  risk of infection is increased.  It is not clear that adding high flow nasal oxygen makes this worse.  However, at a flow of 40-60 lpm if the patient coughs, model studies have shown some additional movement of particles in the room.
Healthcare worker infection from nosocomial transmission of SARS CoV-1was associated with lack of adequate infection control precautions especially in the presence of  aerosol generating procedures. By definition this would also include HFNC. However, the risk of health care worker infection from HFNC was reported to be substantially less (8%) compared to intubation (35%) and NIPPV (38%) (Raboud et al. Plos One 2010). Moreover, placement surgical masks over a HFNC reduces the emission and dispersion of coronavirus bioaerosols (Leung et al. Nat Med 2020)