Have we ever seen Kang go to war against any of Marvel's big alien empires?
I started thinking about that because of Avengers: Earth's Mightiest Heroes. When Kang first arrives, he's trying to avert the death of Earth in the Kree/Skrull War because of a decision Captain America will make. His solution, besides killing Captain America, will be to provide Earth of the early 21st Century with the technological advances it needs to defends itself from his these star-spanning empires. Of course, he's going to do that by conquering the entire world and ruling. I know, it's shocking that Kang the Conqueror would turn to conquering as a solution.
The Avengers did defeat Kang, and took care of the Kree and Skrulls themselves, but it left me wondering if he'd faced off with them at other times. I'd imagine so, if only because one usually doesn't build an empire without fighting and defeating other, preexisting or contemporary empires along the way. Also, if we're going with the version of Kang that likes a challenge, then at some point he'd have tried the Kree Empire.
On the one hand, fighting an empire that spans a galaxy presents a certain set of logistical challenges. Reinforcements at crucial points, communication, supply, then throw in the fanatical aspect of the Kree, where you'd have to crush every single world. By comparison, fighting only a select group of people on one planet is a fair amount easier, given that the Avengers aren't typically much for hit-and-run tactics. You'll know where to find them (or how to draw them out). On the other hand, the space empires rely at least in part on having overwhelming advantages in firepower. Which, if we're talking 20th Century Kree, or 35th Century Skrulls, they probably won't have that when they face Kang, direct from the 41st Century. The Avengers are used to facing alien races who are far more advanced than Earth. They're used to being underdogs and winning anyway.
I'd actually be interested in a story where Kang uses the various alien empires to further some plan of his. Maybe he thinks they'd be more of a challenge if they're united, so he engineers conflicts between them until one stands supreme (which would have been the Inhuman-ruled Kree by the end of Abnett and Lanning's cosmic run, but I have no idea who it is now. The Spartoi, maybe). Or he takes power in some disguise, then throws one of them at Earth to test the Avengers, or even to toughen them up for when he arrives with his true forces.