FlexSim 2016 Update 1 (16.1) or later should work with the Oculus software with either the DK2 (dev kit 2) or the CV1 (consumer version 1) headsets. These versions of FlexSim will not work with the old Oculus Runtime drivers; you need to use the new Oculus software that includes the Oculus Store.
FlexSim 7.7 and FlexSim 2016 (16.0) work with the Oculus Runtime 0.7 or 0.8 with the DK2 (dev kit 2) headset. These versions of FlexSim do not work with the new Oculus software or the CV1 headset.
I just tested FlexSim 2016 Update 2 (16.2.2) with a DK2 using Oculus App Version 1.10.0 and it is working fine.
The top of the Oculus software has a warning saying that DK2 is not supported on the Oculus platform, but it still works fine with FlexSim:

It is possible that a different version of the Oculus software doesn't support the DK2 entirely instead of just giving a warning. You could try searching the internet for suggestions on how to resolve that, but FlexSim should be working fine. Here is a webpage with a question about DK2 not working with Oculus Home 1.8, but the comments seem to indicate that it still works fine.
Phil BoBo
Sr. Manager, Software Development