First of all just to let you know you can not install software to a flash drive.
You can save the software not installed to the flash drive.
So that would be the .exe or .msi that you ran to install H&R block, but I don't think you really need to do this if you just want to back up your return.
And after an internet search looks like the only way to really back up you return is to save as a PDF which you then can put on a flash drive.
http://community.hrblock.com/t5/DIY-Products/ho...
I did the exact same thing with my returns this year using Simple Tax Return. When I was done i submitted the return to my government and I was able to save it as a PDF which I then saved to my onedrive.
Let me know if you need more clarification.