I found a job where I write furigana above kanji.
振る is "to shake." 仮名 is kana. This word refers to furigana, which is the little kana that's put next to kanji for the people who don't use WaniKani and can't read anything. As to why it's called "shake kana"? I have no clue. Just imagine putting little kana next to kanji and watching them shake around, though, and you should be good to go.
The readings are 振る and 仮名 put together into one. If you know those words, you won't need no furigana to help you with this word.