Never the facts get in the way of a good story
Well he wasn't part of the project in the film, he was involved in breaking the Lorenz ciphers so no reason to include him. That said, there was absolutely no reason at all for them to have included John Cairncross, since there's no evidence that he ever met Turing, let alone the other ludicrous plot elements so it wouldn't have hurt to include Flowers in the highly inaccurate plot of the Imitation Game :)