The flu jab is tailored for the specific strains of flu that are predicted to be circulating during the next year. It takes a year to identify these strains and then manufacture the jab. There are always several different strains of flu circulating in any one year, so not all the flu strains are covered.
Since the COVID19 stain is a mutated cold virus, not a flu virus, it is not covered by the current flu jab, and any jab will take around a year to produce.
Having said that, it appears that the COVID19 is mild in the majority of cases.
Remember swine flu? Most people with it went around coughing over everyone else because they thought they had a cold, and didn't actually realise that they were spreading the flu. I suspect that the same will happen with COVID19.