Crown-of-thorns is also known as Kiss-me-quick plant in Japan.

... BWAHAHAHAHAHAHAHAHAHA! I hope Kanda decides out of idle curiosity to google the meaning of her gift after Kai more or less introduced her to the concept of flower language, because otherwise she'd probably be very confused when Ookuma's misunderstanding drives her to awkwardly attempt to "rectify" the situation.

Where in the manga does it explain the meaning of the crown-of-thorns? Are readers just expected to know this?

And did Kai lie to Kanda about the meaning or are there just additional meanings?

CaesarsSalad said:

Where in the manga does it explain the meaning of the crown-of-thorns? Are readers just expected to know this?

And did Kai lie to Kanda about the meaning or are there just additional meanings?

the language of flowers is pretty popular in girls and romantics, as it can get a point across without words. its most likely just one of the artist's interests peaking out since its not a super popular 'study'
Kai didn't lie, but might not have known the double meaning. he never says to give Ookuma the flower. the flower was supposed to give Kanda "strength" to tell the truth, but Kanda gives it to Ookuma anyways when she fails, and Ookuma, being a huge romantic, finds the name's double meaning instead