You must remember that with a Naval service record, it is not a precise record of someone's movements, rather, who was responsible for making sure he was paid etc.
Pembroke was the name of the naval barracks at Chatham. They would have been what is known as his 'parent establishment' and would have made sure that he was paid etc, until he could be taken over by a new 'parent' - your relative obviously arrived in Egypt in May 1944 when Nile took over as being the 'parent'. This also explains why some names appear in brackets after others. The first name is the 'parent', who looked after all the paperwork, the name in brackets was where he actually was.
He would not have flown out - that was strictly for senior officers. He would have taken passage on a ship en-route to Egypt, presumably in April 1944: unless mentioned anywhere, that would be very difficult to identify. During this time he would have remained 'on the books' of Pembroke.
