The title of your post (taken from the article) is wildly misleading. More accurately: there is a correlation between having a flu vaccine and not being as vulnerable to severe covid 19.
I doubt this is the same flu vaccine we are using- there are hundreds of flu viruses and the ones affecting the UK this winter coming are almost certainly a somewhat different combo from the ones affecting Italy last winter. This is the Italian article. It's conclusions are complicated by the fact that the Italian outbreak was highly localised at first, in the region with less flu vaccine uptake. Still it's findings are suggestive.
www.mdpi.com/2076-393X/8/3/535/pdf
I would bet a very large amount of money that the flu vaccine has no effect on Covid immunity. It's theoretically possible if one of the flus in both of those vaccines is a coronavirus but so far all the research is saying not.
It's almost certainly a combination of factors; a big one is probably that having your body ravaged by flu leaves you more vulnerable to a subsequent illness.
Not really surprising data, this is why they push the annual flu vaccine so hard, but still welcome news.