return to school to suffer through intensive courses on the weapons Rothana, Kuat, and others had built for the Kaminoans to equip the Grand Army, and on the weapons Baktoid, Hoersch-Kessel, and others were engineering and producting for the Separatists. On graduating he had supervised a brain trust of research experts who reported directly to the upper echelon of the Republic military.
Catalyst: A Rogue One Novel, Chapter 3

Finally, sometime after the Empire takes over, the Strategic Advisory Cell is absorbed into the Tarkin Initiative, and Krennic becomes Director of Advanced Weapons Research:

... [Krennic's shuttle] is on Tarkin Initiative business, with an Imperial advanced weapons director aboard.
Rogue One Ultimate Visual Guide, page 24

I doubt that the change to the Tarkin Initiative required knowledge on military tactics, as the Roguesecure an audience with the Emperor. 
In a highly militarized system of government like the Empire, any senior political position undoubtedly carried with it certain military command. Krennic did wear a uniform and had a certain number of troops at his disposal. If he succeeded with his machinations, he will of course command an even larger part of the Imperial military.
Finally, the reason for his death is being at wrong place at wrong time, and of course being Tarkin's rival. Both Tarkin and Krennic display certain psychopathic traits, similar to Emperor Palpatine himself. Either of them would not hesitate to remove any obstacle to his ambition, no matter the cost. Later, a convenient excuse would be found, like Krennic's supposed guilt for Rebels stealing plans for the Death