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I often see, what I refer to as, implied erhua written in shop names, advertisements, on menus, etc. Take the following for instance:
You'd rarely ever hear gé pì read without erhuaization. So the idea is that, although 儿 is not written, it is certainly implied.
Technically it would be considered to be written incorrectly, as the example above should be written 嗝儿屁. But is this some kind of phenomenon that I'm half aware of?
There is such text in the 凡例 section in 《现代汉语词典》：
书面上有时儿化有时不儿化，口语里必须儿化的词，自成条目，如【今儿】、【小孩儿】。书面上一般不儿化，但是口语里一般儿化的，在释义前面加‘（~儿）’，如【米粒】条。……
The text shows how 儿化 is shown in the entries and explanation. The words with 儿化 are mainly divided into two groups: 1. Words that are sometimes written with 儿 and sometimes not, but are always pronounced with 儿化 2. Words that are usually not written with 儿, but are usually pronounced with 儿化.
It shows that there are words that would not be written with 儿化, but would be pronounced with 儿化. Each word has its own tendency as whether it would be written with 儿.
(Note: all 儿 in the quoted text showing 儿化 are in small font in 《现代汉语词典》.)
"嗝屁" sounds like Beijing dialect. It isn't in my Mandarin Chinese dictionary("Modern Chinese Dictionary"). I'm going to just talk about normal situations: in Mandarin Chinese.
"儿" usually should be write. In dictionaries(and articles too), it shows. For example: 没准儿, 没影儿, etc.
How to give it a pinyin? Don't add "ér" above "儿", but add a "r" above the previous Chinese Character, such as the pinyin of "没准儿" is "méi zhǔnr".
儿化音 is frequently unwritten, given that it has no effect on meaning in almost all circumstances (rare exceptions like 水 water vs 水儿 ink notwithstanding).
You could even argue that knowing where to insert the unwritten 儿 while speaking acts as a kind of shibboleth for people from regions that use a lot of 儿化音. But perhaps that's reading too much into it.
嗝屁 is an informal word. You don't expect a strict structure in informal usages.
