The "Your Answer" textbox seems to be eating the flagging dialog as shown in Figure A.
This has been fixed yesterday and is available since
rev 2245 on meta and
rev 1606 on the network as part of this bugfix.
While this is far from a solution; a usable workaround to this problem is to ensure the view is scrolled up as much as possible when you click on your flagging options (so what you click is at the very bottom of the screen). This ensures that the stuck text box is far away from anything you might want to click on the next screen.
Rotating the screen from portrait to landscape (after opening the dialogue) can also shift the text box around; potentially allowing the dialogue to be revealed.