Dickon was a bit overboard, his father had already betrayed an oath to the Tyrells (who supported Daenerys) and when given the chance to take that back chose death. Hardly sport either when they just got done sacking Highgarden, which was behind Daenerys at that point
in fact the whole burning of the lannister army - she just set them alight and f**ked off.
So using the weapons she has available to her in the middle of a war makes her insane? I guess every character who has fought in a war in this series is insane then. She didn't f**k off, either, she was there until the very end of that battle. Not to mention that the majority of Drogons attacks were focused on taking out carts, and any soldiers burnt after that initial breaking of the line were collateral damage.
She burned that magi on the pyre that resulted in dragons - there was nothing in burning that woman expect for revenge (sport).
I'll give you this one.
Her first reaction when negotiating to purchase the unsullied was to burn the bloke selling them to her. For no reason other than he said a few things he didn't think she would understand.
Actually her first reaction was to tell the Unsullied to kill every master, but to harm no children and free every slave. That guy was a master, so he got toasted. He was dying either way on that day, showing zero respect to her in the lead up didn't help his cause at all.
If she flies off the handle when she finds out Jon has a greater claim to the throne than she does I'll happily jump on board the "she's a mad bitch" band wagon, but until then nothing I've seen tells me she is going to be anything like Aerys. Viserys on the other hand was a grade A merkin.