I haven't seen this structure before, but I'm extrapolating from things I know. nanbon =　なんぼん =何本 = how many [things that are counted with 本] nanika = なにか=何か= something If なんぼんか means "some number of things counted with 本", then なんぼんかのはなwould mean "some of the flowers" ... are paper? Is that the kami? It's really hard to tell with just hiragana. But since this is just my best guess, I plan to follow this question in case a native speaker or someone who's studied longer has a better answer! ＾＾；

なんぼんかのはなはかみです＝何本かの花は紙です＝Several/Some flowers are (made of) paper. hon/bon/pon is a counter suffix<助数詞・じょすうし> which is used when we count slim things. なに(what / how many)＋ほん＋か(an unsettled particle)→なんぼんか＝several (slim things) ※鉛筆<えんびつ>は何本<なんぼん>ありますか。＝How many pencils are there? 　鉛筆は何本かありますか。＝Are there several/some pencils?