You could have picked a better time, bit hazy in here and google seems reluctant to give simple answers lately . . .
I didn't pick the time of your reply, you did.
My charger says 0.55 amps max output at 5v so that's 2.75 watts so would need to run for just over 40 minuets to consume 6615 joules.
That's assuming a perfectly insulated coffee cup so the time would be shorter, maybe half an hour for a travel mug and 5 min for a glass mug, chargers are generally into the 90% efficiencies so not much lost there.
. . .you can pick one up on ebay for something like 50c that will run for about half an hour on the heat from a cup of coffee and put out enough power to put about a days worth of charge into a mobile phone . . .
I haven't double checked your math or assumptions yet, but...
Would the 5 minutes of charge that you are going to get at 2.75 watts will be enough "to put about a days worth of charge into a mobile phone"? Or the half hour? Or the 40 minutes? My phone usually takes longer than that to charge (and I rarely get a full day's use from a single charge).
Furthermore, your calculations assume that you use the full amount of energy from the mug (minus losses), 6615 joules, within the given timeframe. It seems to me that the heat won't move through the sterling engine that fast. As the heat moves through the engine, the thermal differential will drop further reducing the power output.