It´s hard to see the flags, and I checked the rest of the pictures that Carl Størmer took to see if he caught the same flags from another angle, but no luck. The digital museum website where I found all the pictures does describe your linked picture as: "Gatebilde med mange mennsker og flaggdekorasjoner på stolper. Fru Movinkel, født Sverdrup, midt i bildet. Muligens Karl Johans gate, Oslo"

Translation: Street photograph with a lot of people and flag decorations on poles. Mrs Movinkel, born Sverdrup, in the center of the picture. Possibly Karl Johans street, Oslo.

So as to the where, the digital museum points us to Karl Johans street, Oslo, Norway. The when, in the 1890's. Can´t find a specific date, but will keep looking.

As to the what, the most likely guess here is that it is the Norwegian union flag. That is, in 1890 Norway was in a personal union with Sweden, so the flag flown in Norway was the same as the modern day one, but with a small Union Jack-like symbol combining the Swedish and Norwegian colours. Here is a picture from 1899 of the flags: (it´s no wonder the union dissolved with such an ugly union jack copy)

https://upload.wikimedia.org/wikipedia/commons/thumb/3/3f/Flaggplansje_1899_copy.jpg/800px-Flaggplansje_1899_copy.jpg?1515076177349

Note: this picture is from 1899, which is when Norway was trying to "purify" their flag and take away all union symbols. (quite successfully). The flag used in 1890 is still the one which the picture I linked describes as "Flag of the Royal Norwegian Navy".

If you zoom in on your picture, you can just make out, on the leftmost of the closest flags, the bottom triangle on the little union symbol. From the design of the big cross on the flag, it is the Norwegian flag, but with the little union symbol on it.

Norwegian digital museum website with all the pictures from Carl Størmer: https://digitaltmuseum.no/011013321405/gatebilde-med-mange-mennsker-og-flaggdekorasjoner-pa-stolper-fru-movinkel

Edit: words and added explanation of flag picture