I'm by no means an expert here, but as far as I understand, you can flash it either using the CapsuleApp.efi (i.e. from the onboard EFI shell), or using DediProg, if it's not getting as far as the EFI shell. The BSP Build Guide has instructions on that, see Section 10 (https://communities.intel.com/servlet/JiveServlet/downloadBody/21882-102-1-25153/Quark_BSPBuildGuide_329687_001.pdf).
Out of the curiosity - how did you get the board to that state? I'm currently preparing to try the newer 0.8.0 BSP on my board and as long as I haven't done many such FW upgrades yet, I'm gathering the information around on what can go wrong to make sure I'm prepared :-)