The use of deflated in your passage is not related to unhappy.
In the military, officers are expected to conduct themselves in a certain way. This tends includes a posture which is rather stiff: straight back, stomach in, chest out, chin up, facing straight. Maybe you get the picture that the posture is pumped up.
The military also has many rules of conduct which some people find comforting since it's all spelled out, there's little left to nuance, and requires less thinking.
When a soldier/sailor is allowed on furlough it is basically their time off and they are allowed to wear civies, normal, non-military clothing. They are still expected to behave well, though more relaxed. This is in contrast to being on leave when they may still be required to wear military dress and behave as if they are on the job.
The author is trying to convey the feeling that Alan Dunn is more relaxed in the scene, and possibly he may feel out of place given the military rules of conduct are not set as boundaries.
This picture of Alan Dunn is further confirmed by the passage
tells Jim, rather unconvincingly
Colonels are never unconvincing, leaders always show confidence. Bear in mind, Alan Dunn, is a headmaster, the leader of a school, he is compared to a colonel, a military leader of soldiers. The author is also making an allusion to the stereotype that civilians are more relaxed and less intense than military personnel.
Tall spare man with a neat moustache
To picture Alan Dunn, you might want to think of Basil in Fawlty Towers.