Translation:Everyone usually has flu in winter.
for those who might be interested, I'd just like to bring a nuance with the use of "thường xuyên" vs "thường". in the initial sentence "mọi người thường xuyên bị cảm cúm vào mùa đông", the speaker implies that a lot of people are sick during winter. if we change "thường xuyên" for a simple "thường", the speaker will then mean people are more often sick in winter in comparison to other seasons.
"Everyone usually has flu in the winter" is correct. It should not be rejected. The translation DL gives without "the" is correct. Also correct are: "Everyone usually has the flu in the winter" and "Everyone usually has the flu in winter." There are four possible choices with respect to the use of "the"; any of these should be accepted.