How is "biang" as in "biáng biáng miàn" pronounced in other dialects? To my understanding, "biáng" is not a sound that exists in Mandarin, though there's some argument on the hypothetical phonological possibility of such here. One might assume therefore that it is a character either unique to or else created within Shaanxi dialect (given the alleged origins of the word). If such a character is read by a speaker of another dialect, how would it be pronounced? How might, say, a Cantonese-speaker or Hokkien-speaker read it?
I don't think this is the answer you want but it's the answer you're getting, at least from me.
明末洪帮图符研究 on the Wikipedia page for Biángbiáng面 notes:

流传于四川盆地的两个妇孺皆知的复杂汉字“”和“”，其内部结构与“缺字图片”字十分类似。类似结构的汉字流传于10多个省市，300多年来均有出现，却仅限民间相传，从无传统典籍收录。
重庆一带的“”字和四川一带的“”字，均念为“ zuí ”，即当地方言中的“贼”，意指强盗。为了方便记忆，它们同样也有歌谣对应[注 8][注 9][注 10]，在当地乡村中人人均能背诵。[14][13]

According to:

余云华. 怪字“”、“”、“”考. 民俗研究. 2002, (02).

and

王纯五. 洪门·青帮·袍哥——中国旧时民间黑社会习俗. 四川: 四川人民出版社. 1993: 71. ISBN 7-220-02058-9.

The biáng character is used for the pronunciation zuí in Sichuanese and Chongqingese.
The characters, though, have slight variations:
Here's the Chongqing variation

重庆一带zuí字


and the Sichuanese variation:

四川一带zuí字[13]


According to the materials they mean the same as 贼 or thief.
Sichuanese/Chongqingese words like:

贼呵呵
贼脚摸手
贼脚摸爪
贼眉贼眼
贼娃子
贼货

Could, in theory, be written with biáng instead of 贼.

Funnily enough, though,《广安方言与民俗词典》from Sichuan has also recorded an entry for:

biáng

which they have defined as:

普通话中无“b-i-ang”发音，属于群众自创方音。象声词，本义指用力扯面中面条击打案板之声。生活中常作为口语化的象声词，如巴掌打在脸上的声音、面积较大的东西摔在地上的声音等。为了方便记忆，民间还有此字歌谣：“一点一横长，二字下来口字方，两边丝绕绕，中间马大王，你也长，我也长，心字底，月字旁，打把金钩挂衣裳。”

The rhyme matches the footnote on Wikipedia for:

重庆一带“”字歌谣为：“一点一横长，二字下来口字方；两边丝绕绕，拉根板凳来坐倒；你也长，我也长，中间夹个马儿郎；心字来打底，月字来包墙，打个金钩银钩挂衣裳。”

perfectly.

So, in Sichuan/Chongqing, is it zuí or biáng?
I guess it depends on the context.

Lastly, according to 辞书收录 on the Wikipedia page for Biángbiáng面:

《都市方言辞典（陕西卷）》[16]收录此词条，并详细介绍了相关饮食文化：
 biáng[piaŋ24]     ①“儿面”的biáng。
②指人死掉，含庆幸语气：狗日的这回才～了。
面 biángbiangmiàn[piaŋ24piaŋ24-31miã55] 详见下边词条
儿面 biángbiangrmiàn[piaŋ24.piẽr miã55] 陕西最爱吃的面食之一……

It would go to show that the majority of dialects would follow the rising tone of [piaŋ24] because after all it is a 陕西 thing.