The word Fluse/Flusen is one of the words, that exists in two variations. Here are other examples:
The feminine form ends with -e and is standard German in all regions where German is spoken.
The masculine form ends with -en and is not so frequently used as the female form.
The further you go to the south, the more often you will hear the masculine form.
In Duden the word »die Karre« is marked as besonders mitteldeutsch, norddeutsch, »der Karren« as besonders süddeutsch, österreichisch
In Duden »die Socke« has no regional marker, but »der Socken« is marked as süddeutsch, österreichisch, schweizerisch
same status as Socke(n)
In Duden »die Schraube« has no regional marker, and »der Schrauben« is not listed at all, but it exists in Bavarian dialects and many dialect speakers (like the owner of the Viennese tool shop) even use it when they try to produce standard German
Here is the situation similar to Schraube(n): The masculine version exists in Bavarian dialects and is not part of standard German. But still some people use it in a standard German context.
The density of masculine variations of words that match this pattern, is very high in Vienna. Maybe it is high elsewhere too, but I lived in Vienna for many years (1997-2016), and still visit this city approximately twice a week to meet friends (except now, during the corona lockdown), so I know the language spoken in Vienna very well.
And guess who else lives in Vienna? It is Isabella Rau, the author of the sentence in question. I didn't read her book »Männer und andere Ballaststoffe« (»men and other fiber«, »men and other ballast materials«), so I don't know if she willingly uses a language that is close to the colloquial speech of Vienna, of if she just used the word because she is more used to the masculine form than to the standard feminine form.
About »die Fluse« being a Low German word. (Reaction to comments)
People in Austria are much more exposed to variations of German spoken in northern regions of Germany than People from Germany are exposed to Austrian specialities. Austria has 8.9 million residents, Germany has 83 million. So, the market for books and magazines is dominated by speakers of German German. Even books and magazines produced in Austria are not published in Austrian German, but in German German (with some extremely rare exceptions for books, but not a single exception for magazines).
So, when you are in Vienna and buy and read a book or magazine, then you always will be exposed to the vocabulary that is in use in Germany, including vocabulary that has its origin in Low German. It never happens the other way round: When you are in Hamburg and buy any available book or magazine, you will never ever be exposed to Austrian vocabulary.
This means, that almost everybody in Austria is fluent in two variations of German: The Austrian variation that is used to talk with other Austrian people which is our first language, and the German variation, that we use when we write. And sometimes, without any intention, we use words from one of both variations when we produce sentences in the other variation.
So, using a word that comes from Low German in a standard German text produced by a native speaker of the Viennese dialect (which belongs to the Bavarian dialects) is not so strange as it might seem at first glance.
About »der Flusen« not being listed in any dictionaries:
You also will not find »der Schrauben« or »der Noppen« in any dictionary, but they are still used in real life. Not to be listed in a dictionary does not mean that the word doesn't exist. Most dialect words are not listed. For example the very common word rean is not listed in any dictionary because it is not standard German but Bavarian.