I was musing similar, but I've only probed the basics, and not actually made rules yet. Though I had plans to do it on a second go-around of Kingmaker, and would love to see advice. That said, with my running Kingmaker, here are the things I noticed.
The big road blocks to keep in mind are that you'd need to custom tailor completely new encounters from Kingmaker's army system.
Troops don't have as hard a leveling system, as they are built a bit more like creatures, so one would need to create a custom table for keeping track of troop stats. But on a level, troops seem to be modeled as a permutation of the GM Core's creature creation rules, so practicing that would be a start, from there you'd have to standardize what abilities you want. For Kingmaker, you'd probably want to bring this system to at least level 17 for this, but depending on how much your party does random battles and explores, you can extend up to level 20.
Battlecry!'s troop rules don't accomodate Kingmaker's integration of equipping your army with special things like limited-use potions, magic weapons, or magic armor. So you'd need to figure an upgrade system within the Kingdom building rules. Recruitment should work fine, I think, but figuring what bonuses can be granted a troop will take some playtesting.
Then there's figuring out siege engine integration... Whether an army of siege engines is needed to get that many siege engines available, or whether you should instead mod one of your troops to being a siege engine instead. If the latter, you'd probably have to modify the cost of siege engine troops to be cheaper kingdom building side.
As for army allocations, I'd probably recommend letting one army equal troop unit per PC, though, as an army is thematically feeling bigger than a troop in its scope. Enemy armies would likely gain similar growth. Though playtesting would need to be done to figure what the right amount of armies is, especially for variable-size armies.
The most unfortunate thing is that all army combats would have to be swapped for troop combats in this event, and I lack experience with troop combat, you probably would too. You could let the findings of your early level troop combats help you scale for the late level ones. Encouraging some testing random battle troop activities might be a way to get information to better gauge what you can get away with, if your players are down with that.
I'd recommend running some simulation gamaes to see how troop combat works. One aspect I considered is using Valerie as a tool if your players recruit her. She fancies herself a knight, and would not be unlikely to take interest in things like Strategy games. Asking her to request your general to play a tabletop war game with her to hone their skills, or if she is your general, to help fine tune her plans, would be a way you can simulate troop combat without risking player resources. The best part is you can set parameters under- or overestimating rival factions to represent their assumptions of their abilities. (Amusingly enough, according to Grand Bazaar, there even is a strategy game called "Kingmaker"
