[Greece]

He is using iPhone 6. For some reason, I suspect that he is flirting with one of his female workmate. Is it legal if I spy on his mobile phone? And how can I do that?

Obviously spying on someone's convo without their permission is illegal. However, if it's sms it's using your reception. Ideas:

1: Simply check his messages on his phone
2: Download WireShark and connect to monitor your local wifi and try to capture packets (only will work if he's using iMessages from the WiFi and even then I think they will be encrypted.

The most simple option you have is to just check the messages on his phone ;p