Yes, lots/most don’t get tested for the flu, but the 0.1% is an estimated rate - the 0.1% is confirmed deaths / (confirmed cases + estimated # of cases -> much larger group)
So far, COVID-19 has a higher death rate among confirmed deaths/illnesses than confirmed deaths/illnesses for the flu.
For the flu, the CDC seems to be lumping estimated flu and pneumonia deaths together, which would make the flu number look larger.