Does English allow alveolar flap [ɾ] at the ends of syllables? If yes, how to syllabify?

Question

Prompted by this question: How to syllabify “very” or “merry” etc in British English?, I found the linked question interesting and it was a very good question but it did not get much attention, therefore no answer.
That question is about the syllabification of "very" and "merry" in British English and my question is about words like better, bitter, butter in American English.
In most American Englishes words like better, bitter, butter are pronounced with an alveolar flap [ɾ]:

/ˈbɛɾɚ/
/ˈbɪɾɚ/
/ˈbʌɾɚ/

The linked question says there should be a consonant after vowels like /ʌ ɪ ʊ ɛ/. Take "butter" /ˈbʌɾɚ/ as an example: if I put the syllable boundary after the vowel, then there is no consonant after it: /ˈbʌ.ɾɚ/ but if I put the syllable boundary after ɾ then the flap comes at the syllable ending position: /ˈbʌɾ.ɚ/. In an answer to my previous question (What's the difference between /t̬/ and /ɾ/ in American English?), TaliesinMerlin wrote that alveolar flaps at the end and beginning positions "sound odd", but they didn't say if English allows them or not.
My question is: Does English allow alveolar flaps at the ends of syllables? If it does, then how should one syllabify them in the following scenarios:

/ˈbɛɾ.ɚ/ or /ˈbɛ.ɾɚ/
/ˈbɪɾ.ɚ/ or /ˈbɪ.ɾɚ/
/ˈbʌɾ.ɚ/ or /ˈbʌ.ɾɚ/

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Someone on Reddit told me that the flap should be "ambisyllabic" but I don't understand that. There must be a way to syllabify those words. It isn't impossible to syllabify them. I would like to know how they are syllabified.

Decapitated Soul · Answer

In his Syllable Structure: The Limits of Variation, San Duanmu argues that the [ɾ] has to be syllabified as the coda of the preceding syllable because word-final [t] can flap as in sit in, but word-initial [t] can't. So you can't say time with a [ɾ] in 'a time when ...'. Another example he gives is mighty; he says that ‘the [t] in mighty is flapped, and so the syllabification must be [maiɾ.i] ...’.
Another similar example is [maɪɾˈaɪ]: it can only be interpreted as might I, not my tie because word-initial [t] can't flap.
In the book, he also explains the ambisyllabicity principle on page 60. He represents ambisyllabic consonants by underlining them (e.g. potato):

Does English allow alveolar flap [ɾ] at the ends of syllables? If yes, how to syllabify?

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