In some parts of America, do people commonly use a flap after /n/, e.g. /ˈwɪn.t̬ɚ/?

Solution 1:

Phonetic literature that I have seen typically describes this as a nasal/nasalized tap/flap rather than a nasal consonant followed by a tap/flap.

The frequency of this pronunciation varies by dialect, but I am not aware of any dialect where [nt] with non-flapped t has been completely eliminated. In most dialects, [nt] is a possible realization of /nt/ even before an unstressed syllable.