It's pronounced jif. How do I know? Literally IT/computer person I know who works with computers for a living says jif. And I know a lot of people. As for rules, I don't care. Anything goes. Have fun, and don't take it too seriously.
.GIF is an acronym for Graphic Interchange Format and I say that it is to be pronounced as written. My reasoning is that more people I know say GIF and there is no J in the acronym or the full written out term.
G can be pronounced as a 'j' sound. In the word 'badge', the g at the end is pronounced like a 'j' when followed by a vowel. In the file name .gif, g is followed by a vowel, therefor making a j sound. Can you defeat my amazingly illogical logic?