Just a couple of thoughts...
Cullen would have some military experience, experience with Templar training and tactics (good to use this knowledge against the Red Templars), has experience dealing with demons and abominations and is loyal to the Chantry and the Divine. He has some leadership skills as a Knight Captain, and apparently these developed further in the interveneing years.
It would make sense that as a fledging organization, Cullen might be a viable candidate for a military advisor. As the Inquisition grows, if his skills are not sufficient, I am sure they could find a replacement.
Besides, the word advisor is just that - he can advise, but the Inquisitior does not presumably have to accept his advice. He is not a General afterall.
His military experience may be lacking, but I am not sure the Inquisition is solely a military campaign that can only be won or lost with armies.
In the Inquitisiton, it seems there wil be lots of random battles, in cities, in the country side, in towns. Perhaps Cullens experiences in cleaning up Kirkwall will help.