I suspect it is indeed possible to flip BC6-7 blocks with much less work than a full decompress and recompress, but it's still no picnic and is much more complex than flipping BC1-5 blocks.
First of all, BC6-7 have a variety of modes that can be selected per block. The modes have completely different binary layouts, so you'd pretty much have to write a different flip routine for each mode (there are ~20 of them altogether, IIRC).
Another difficulty is the partitioned modes, where the pixels in the block are partitioned into 2 or 3 subsets, each with its own RGB line segment. The partition must be chosen from a predefined set; the ones for BC6 can be seen here. The problem is that this partition set is not symmetric under vertical flips. However, I suspect it is symmetric under some combination of vertical flips and interchanging the two subsets. For example, looking at the partition #22 (6th row, 3rd column) at that link, there is no vertically flipped version of it in the table, but if you vertically flip and interchange 0s and 1s, you end up with the partition #9 (3rd row, 2nd column). I haven't verified that every partition can be flipped this way, nor have I checked the ones for BC7 (which also includes partitions with 3 subsets).
Even if that works, you're still not home free. In BC1-5, the order of the two endpoints of the RGB line segment was used to switch modes, but in BC6-7 the order of endpoints is chosen to fix one bit of the per-pixel indices in each partition subset. Therefore if you change the partition around you might also have to swap the order of endpoints.
And last but not least, in BC6-7 the endpoints are often delta-compressed (i.e. one endpoint is stored at full precision and the others are stored as lower-precision deltas from it). Swapping partition subsets and endpoint order will switch which endpoint is the high-precision one, so you'll have to shuffle the low-precision bits around and negate some deltas.
All in all, it doesn't seem like there's any fundamental showstopper (though I haven't actually written the code), but it sure would be a lot of work to flip or rotate these formats. If possible, I'd recommend flipping the images in your art pipeline before they get compressed.
(BTW, the fullest specification of BC6-7 I've found is the ARB_texture_compression_bptc spec; I also wrote a blog post about the BCn formats awhile back.)