There's not really a huge amount of everyday writing that has survived form the high ancient Egyptian kingdoms, before the later developments of Demotic script in (c. 7th century BC) and Coptic (c. 2nd century AD). One exception is the Deir el-Medina village which was the home of the craftsmen who cut and decorated the tombs in the Valley of the Kings during the New Kingdom, where archeologists have discovered tens of thousands of private documents such as letters, reports, teaching exercises, religious texts, and legal texts, dated to c. 1275 - 1075 B.C. Some of these are papyri, but mostly ostraca, i.e. shards of pottery or limestone. The Deir el-Medina community was probably more literate than the average Egyptian working class hamlet, but it is an unusually rich source to the everyday writing in ancient Egypt.

These documents are written on the so-called hieratic script which was developed alongside hieroglyphs for the scribal practise of writing on papyri and other less-monumental media like cursive hieroglyphs, but hieratic is much more cursive and has more unique signs. It was simpler, less 'flashy', and faster way to write than monumental hieroglyphs that were painstakingly carved to be just as much aesthetically pleasing as communicative. Structurally, however, hieratic is not different from hieroglyphs: here's a few example of the hieratic derivatives from hieroglyphs. Hieratic is therefore a mixture of logograms - i.e. symbols that will have one meaning, such as 'sun', 'mountain', 'house' - and phonetic signs - i.e. unililiteral, biliteral, and triliteral signs for one, two, or three consonants respectively; the ancient Egyptian writing rarely indicates vowels. In addition, they used so-called 'determinative' symbols, i.e. when a phonetic sign might be homophonic (words that are written the same but can mean different things), they are added as 'silent' symbols that clarify the meaning of the word. Sorry to keep linking just Wikipedia articles, but the hieroglyph one actually has very good examples to illustrate the logic of hieroglyphs.

So, what this means to your question about slang or vernacular writing - well, firstly, there's really no notably regional differences in Egyptian written language. This is probably due to the centralised nature of the kingdom, and because the writing system was rather complicated, you would only really learn it if you went to the scribe school, and writing remained a skill of only a small and limited class of Egyptians. Secondly, because Egyptian writing was only partly phonetic (and does not really use vowels), slang words could not even be written down in their 'slang' form! Even if you wanted to call a girl chick, bird, babe, gal, or ho you'd still just write down the symbol for 'woman'. We for example have letters where people complain that the regional dialects were so different that a Southern Egyptian struggled to understand what his Northern cousin said, but without these personal accounts we would have never known that dialects existed, because the written Egyptian is completely uniform regardless of the region! So, unfortunately vernacular Egyptian is completely lost to us, opposed to e.g. ancient Greek or Latin, which are of course completely phonetic writing systems. Since Latin had a much more easily approachable writing system than Egyptian, common Romans could pick up writing much more easily and represent words just as they heard them, and thus we have relatively rich records of 'vulgar' Latin through graffiti and such.