This is the 477th most frequent Slovenian word.
slovenski
Slovenian; relating to Slovenia or its language, culture, or people.
Here, 'slovenske' is in the genitive plural, agreeing with 'knjige' (books), and it describes them as originating from Slovenia or written in Slovenian.
Berem slovenske knjige.
I am reading Slovenian books.
In this case, 'slovenska' is in the nominative singular feminine form, describing the flag (zastava) as it relates to Slovenia.
Slovenska zastava je lepa.
The Slovenian flag is beautiful.
Here, 'slovensko' is in the accusative singular feminine form, associated with 'kulturo' (culture), indicating it is the object of promotion.