Both "in flagrante delicto" and "caught in the act" are used and mean the same thing. In general, in legal writing we try to avoid Latin when English will do, but it's often a rule honoured in the breach (too many examples to list!). Since it's an appellate decision, you could chose either. If it were a more informal decision, I would choose "caught in the act". However, note that "in flagrante delicto" also has a sexual connotation (catching one's spouse in bed with someone else, etc. --> catching them "in flagrante delicto")
For reference, here are some Canadian court decisions showing usage of both formulations:
[44] Mr. Bennett [...] was committing an indictable offence and hence the only issue is whether Chen 'found' him in flagrante delicto.
https://canlii.ca/t/2f7qc False confessions easily lead to miscarriages of justice [...]. Except in the rare situation where a perpetrator is actually caught in the act of committing the crime, a confession is regarded as the most powerful, persuasive, and damning evidence of guilt that the state can adduce.
https://canlii.ca/t/jh4fm
peer agreement (net): +2
