A January 2020 US Pentagon study (Wolff 2020) found that the flu shot INCREASES the risks from coronavirus by 36%. "Receiving influenza vaccination may increase the risk of other respiratory viruses, a phenomenon known as "virus interference…'vaccine derived' virus interference was significantly associated with coronavirus…"

Many other studies suggest the increased risk of viral respiratory infections, including coronavirus, following vaccination for influenza.

A 2018 CDC study (Rikin et al 2018) found that flu shots increase the risk of non-flu acute respiratory illnesses (ARIs), including coronavirus, in children.
A 2011 Australian study (Kelly et al 2011) found that flu shots doubled the risk for non-flu viral lung infections.
A 2012 Hong Kong study (Cowling et al 2012) found that flu shots increase the risk for non-flu respiratory infections by 4.4 times.
A 2017 study (Mawson et al 2017) found vaccinated children were 5.9 times more likely to suffer pneumonia than their unvaccinated peers.