All else held equal, does a pot of tea have more total caffeine than a mug? Let's say you have one tea bag and can either brew it in a mug of boiling water, or a larger tea kettle of boiling water. The temperature, steeping time, type of tea bag, etc. are held constant. Assuming you drink all the tea that gets made, would you consume more flavor/caffeine from one method than from the other?

I'm just wondering because even though the amount of tea leaves in the tea bag would be the same, it intuitively seems to me like the water surrounding the bag in the tea kettle would be more hypotonic because there would be more of it compared to the amount of tea, so more tea would come out of the bag overall.
The pot will have more caffeine. 

You are right that the concentration of the final solution is determined not only by steeping time, temperature, etc., but also by the amount of water available to dilute the stuff coming out of the tea, including caffeine. It will reach balance earlier with less water. So more water will get more of the different compounds in tea dissolved. 

For an empirical observation by somebody surprised by the result, see also this question.