I don't believe it is rhyming slang. In the mid-19th century a kite was criminal slang for an illegal message, for example one sent to or from a convict. It then took on the meaning of an 'illegal' cheque...also a bit of dodgy paper, as it were. It might be illegal because there were insufficient funds to honour it or it was stolen and forged from someone else' s cheque-book etc.
The phrase 'to fly a kite' originally meant to pass a dud cheque. Today, sometimes this is called 'paper-hanging', so the idea of not-quite-right paper seems to be consistent and that may relate to actual kites as toys, which were usually made of paper, too.