Grammatically correct sentences (not sure about the meaning) :
Он положил молотые семена льна в свою кашу.
Он положил молотые семена льна в свои хлопья.
What about the word хлопья, овсяные хлопья is used to cook овсяная каша. It is a well known dish in Russia. Other kinds of хлопья are lesser-known.
As far as I understand, "breakfast cereal" is a mix of various kinds of хлопья and dried fruits. This dish has become known in Russia recently. (At least, I can not recall if it was known in my childhood.)
My ex-girlfriend liked it very much, she ate it almost every morning. I myself had never ate it before I met her, not even knew this dish existed.Have no idea what is the correct word for this dish in Russian. I call it кукурузные хлопья.
Злаки and зерновые. These words usually refer to the appropriate plants, not to the things you can eat.