For Scrapies they will (usually) require to put a tag in their ear (what little bit of ear your goats have). This tag will identify where they come from (herd or owner usually) and in the case that one of your goats has Scrapies, they can pinpoint where the animal originated and will then need to enforce their regulations, which is usually to kill all of those animals, including your own in case they are infected, thus 'preventing' the spread.
However, if your goats are registered, they will not need to receive this tag, since their tattoos usually work the same way.
Now, it is obvious that Flower and Blossom do not have Scrapies, so you should be able to get them tagged without any issues (if this is what your state requires) and then be able to transport.
I went through the whole Scrapies thing a couple years ago for 4-H, hate the tags because they can get snagged and caught on stuff and tear the ear, which is what happened to poor Libby who had a Scrapie tag when we bought her.
Each state might be different but that's how it is in MN..