If you can produce a vibrato while singing, you can produce it the same way on a wind instrument. I am a singer and flautist and produce vibrato on the flute (and melodica) the same way as singing. Indeed, I feel like playing a wind instrument is just an extension of singing. But not all flautists are able to do that and there are various mechanical ways for them to produce vibrato. But if you can do it, a singing (diaphragm) vibrato creates the most beautiful tone.
PS There is spam on this thread (and elsewhere in this forum) and to make matters worse, a new post (I just noticed) by default inherits the spammer’s tags. Is there a way to flag spam and bring it to moderators’ attention?