Should I disclose academic misconduct on a grad application?
I don't see what the "bind" is.  You are being unambiguously asked to disclose something, so....you should disclose it.  If you just mean "Oh no, behaving ethically may not be in line with my purely selfish interests": right, this is how ethics usually work.  You shouldn't lie, cheat, steal, injure, rape, murder...even when you think you won't get caught.  That's what "shouldn't" means.  

That they also ask you to explain your failed grades is a good break for you: you should explain carefully what happened.  If at all possible you should enlist a sympathetic faculty member to write something corroborating your story in their recommendation letter.  If you are fully believable then you have a shot that those who are evaluating your application will actually believe you.  They may well think that the professor went overboard and end up weighting the failing grade less strongly than a failing grade that was awarded because you (say) failed the final exam.  In fact, if there is something objective you can do to show that you have mastered the material of that course -- e.g. doing a reading course with another faculty member -- then I strongly encourage you to do so.  

[I'm kind of annoyed to add this but...your academic dishonesty is not in any way protected information.  For all you know, your letter writers could bring it up independently of what you tell them.  Or -- much worse -- when you are N years into your graduate program, your old professor could meet someone in your new program and happen to discuss you.  If it transpires that you were dishonest on your application, that could be grounds for dismissing you from the program.  You sure don't want that to happen.  Sigh -- be good; big brother might actually be watching.]