The Flash/Flex/AIR stuff now has an expiration date on it due to Adobe's terrible handling of the announcements at the end of 2011.
Silverlight is suffering in a similar way to Flex/Flash/AIR as Microsoft's announcements of future directions and developers feeling their investment in Silverlight is now wasted.
JavaFX is late to the party and the latest version is not available on all platforms. Are they targeting mobile nowadays?
HTML 5 is too much hype, not enough unified features across the major browsers. It will get there, but that's not today.
Switching to a completely unfamiliar stack of technology is going to be costly - there's no way you can do any reasonable estimates when it's all new to you and your team.
Personally, I'd suggest starting with technologies you're familiar with, which seems to be Java and Flex and add AIR to that mix.
I'd really push back on the tablet support as I think that requirement is vague, but has a huge impact on the project. I don't see a traditional UI on the desktop working well on a tablet. I'd say the tablet needs its own UI.