The problem being this – when a complex Flash Vector is imported into Illustrator the objects are sometimes broken up into horizontal pieces, aligned perfectly editable and selectable etc. Unfortunately these pieces can show up in printed output. Not ideal.
Solution?

Export the graphic out of Flash with an .ai extension and import it into Corel Draw – then export out again as an .ai file – import into Illustrator and copy and paste it into the InDesign document.
It’s still not perfect – but it will vastly improve the situation.