The only way I was able to do this is through a 3rd party app called "imazing" I'm in the same situation, needing to provide evidence of a call log for facetime. For whatever reason Apple doesn't think it's important or that anyone will need to see their call history or facetime history.
Trust me, the data is on the phone, but Apple doesn't make this accessible to the user. Makes no sense to me whatsoever.
Anyway, I tracked down this software called iMazing installed it on my PC, it shows an entire call history between any individual contact. You install the software, connect your iDevice via USB and you have access to see your call history. However, it doesn't say "facetime" specifically but it does show the time, date and duration of the call between the contact. It allows you to export the data to .txt or .csv, but I really needed more visual evidence than a text document that I could have just doctored myself. I felt the immigration officer wouldn't be too convinced by a spreadsheet or txt file. I just took screen grabs from the software itself. It looks a lot more official as it shows your iPhone that is connected, with your username, your contact with their photo if they have one. You can even pull the data from your backups too. I know a lot of people are having this same issue and need to provide evidence of a legit looking call log. Check it out.