It 'Should' support DX12. AMD has said everything from the radeon HD 7xxx series will support dx12, and since this means Graphics Core Next, of which the Kaveri APUs igpu cores are made of, it suggests that this will be the case.
Of course, I cannot pretend to know the actual answer to this, but I cannot see how the graphics core next cores in the discrete cards will work, while the GCN cores in the APUs won't.
Have to tried contacting AMD and asking them?
Your 270x is a graphics core next gpu and so will support DX12. According to the last thing said by AMD anyway.