I have purchased an Australian flynumber and forward it to my Egyptian mobile number. The forwarding feature working perfectly, but the caller ID doesn't appear even if the caller was one of my contacts, instead my phone display "Unknown".
We send the caller ID as its received, perhaps the caller had their Caller ID blocked. You should have no issues receiving Australia caller IDs as those are guaranteed
I'd also check the flynumber call history to see if the correct caller ID shows up there