As far as I know, the current blockchain is compatible across different operating system as long as they have the same "amount of bits", i.e., 64 bit to 64 bit systems or 32 bit to 32 bit systems would work, but 32 bit to 64 bit systems wouldn't work.
If this doesn't work there is a second option. That is, you can export on your Linux system using the ...
Fallback method which is sure to always work, as it is virtually the same as getting all the blockchain data you'd get from another node, but in one single file.
It's lighter because it doesn't have any overhead for indexing etc.
It can be appended to easily when new data is available.
Slower, because the daemon needs to verify all the data, ...
The current LMDB blockchain is compatible across operating systems. Just copy the files and use them directly. The new one in 0.10 is also compatible across 32/64 bit architectures. That is, the format is identical across ARM32/ARM64/x86/x86_64/Windows/Linux/Android/iOS/etc. There is nothing to convert.
I'm pretty sure you're not going to be able to share a folder on Windows and mount it in a VirtualBox guest Ubuntu, using the blockchain from that mounted shared folder. This is because the blockchain file is memory mapped when opened and I'm pretty certain vboxsf (which is the kernel module that handles the share), doesn't support this.
You could create ...