I just realized that not only the last line of Brachio stamp's sound is a reference, but also the middle lines are referring to Ohma Zio's henshin sound too
Since both Agito and Ryuki reference the episode ending phrase, Faiz should too. It should be "Open your eyes for the next flight" referencing "Open your eyes for the next Faiz". It would also make way more sense as a phrase
I somewhat understand Japanese and I wanted to point out the Hedgehog Stamp sounds different from "Chikuchiku surudoku". So I did research and it's complete quote is "Chikuchiku! Surudoku! Hari tsukisasu! Hedgehog!" (チクチク!鋭く!針突き刺す!)