At any given moment, how much energy is stored in the human body as ATP?
ATP burned per minute is not a useful number because the turnover is so high. 2000 kcal/day is dozens of kilograms of ATP so obviously ATP is turned over more than once a day, but there's probably more than one molecule of ATP being passed around between all the ATP synthases.

This blog claims 250 grams. Taking the estimate of ATP concentrations(1-10 mM) from wikipedia and multiplying by a 60 kg person pops out 150 grams (for 5 mM). The ATP/ADP ratio is about 5 to 1 under physiological conditions, so I'm comfortable leaving out that source of error.

So: Probably a few hundred grams, depending on a lot of things. Which is about .2-.7 moles, for reference. 6-20 kJ is not a lot, in fact even at the upper end of estimates you're looking at maybe 8 dietary calories, and probably more like 3.