Okay, I haven't read the book you have in your example, but having been in the military I will hazard a guess. It's difficult without more background. Military Intelligence (intel for short) is widely regarded as inept, misguided and not smart by the people who must depend on the intelligence to stay alive. Military Intelligence is one of the examples usually given when defining "oxymoron". There may be more to explain why this particular intel officer was laughed at, but on the whole an intel officer making an "educated guess" is pretty funny. All they ever do is guess and somebody else does the dying. A cynical view, I know, and I'm sure I've offended Intel officers everywhere, but that's the perception perhaps not the reality.

I see that the commander is using informal speech with his pilots. Talking in the way you talk when you are very friendly or familiar with someone. Then the intel officer speaks and uses the very,very formal “If I may be permitted an educated guess". This sudden shift from very informal to very formal is enough to be humorous to the pilots listening. It makes the intel officer seem a clown.