IIRC there was a fella that advised knights to run a mile each day in the woods in their hauberk. There was a scene with Toby Capwell running in the woods in a show but bugger if I can remember which show it was.
Believe it was "How to Mount a Horse in Armor, and other Chivalric problems" by Dirk Breiding; was a short clip.
And what the others said. If your stamina is low, don't go straight to armor. What I did was regular treadmill. Then I added wrist and ankle weights. Still haven't done it in armor, but I can't dress myself, sooo.....
If this is just to be used to armor for DoK and such, my advice would be to, as boring as it may sound, put on your armor and just go about whatever daily activities you can in it. If you aren't running at DoK, you don't need to run in armor. I can tolerate 8 or so hours in armor for the day at faire and such, reasonably well, but I'm winded from running in armor after 10 or 15 seconds. I've run in armor quite a few times, and it's not for very long. Like the first 7 seconds of this video (Sir Nathan and Sir Edward running in armor too):
Armor is a very special beast. It's part cardio. It's part muscle mass. It's part ability to deal with being sweaty and warmer than usual. It's part just being stubborn enough to say "no, I'm not taking it off yet, I'm gonna wear it a while longer!" even when you might be thinking "this stuff is heavy!".