How do I avoid shin splints?

There is a lot of research that says strengthening your calves is the best way to fix shin splints. I had them when I first joined the army and then after getting stronger they went away.
I would also suggest switching to a mid-foot strike, and changing shoes to a neutral running shoe with more midsole cushion.
As for rucking, I have found that trying to take Giant Steps with longer strides gave me shin splints more than just walking faster, or walking with short running breaks. You should definitely have a pair of rucking boots. Preferably one with a flexible outsole, because a hard rigid outsole like your issue boots outsole can cause shin splints, plantar fasciitis, and pain in your Achilles tendon when you are moving quickly. You can take a pair of issue boots to a boot shop, and have the toe cup and heel cup removed to give you a pair of boots that is comfortable like a sneaker. You can also have the sole replaced with something more suited to rucking. This way you can have a pair of rucking boots that will last you your entire career. You just have to replace the souls every few years

SPC (Join to see) Go on YouTube and look up Pose Method for Running. That might help and it should also improve your time as well. Just my imput.

My personal experience:
1.) calf-stretch before and after running. Even the night before as well as the morning of. Both the conventional palms-forward, one leg back stretch that we did in formation, and also (actually, for me, more importantly) using a curb to really drop my heel down and get good, long stretch.
2.) sufficient recovery time (we used to run M, W, F). Running on a unit's PT schedule, if you are needing more time than that between runs, then that's hard to address without buy-in from immediate leadership or a temporary profile. If running independently, then build up speed and distance gradually.