No, I believe he is referring to the shape, not the flechettes themselves.
A dart shaped projectile would absolutely work better in a sabot. It will be drag or fin stabilized and not spin stabilized.
Since a lack of spin stabilization is the problem going with a small .22 diameter bullet because the rifling of the larger caliber barrel won't stabilize the small bullets, not needing spin stabilization will help.
That said drag and fin stabilization may not be as precise as you have come to expect. It is more complicated to make a perfect set of fins on multiple projectiles than a perfect bullet. So under MOA accuracy should not be expected. But it may still be much better than keyholing rounds with horrible accuracy.
Another limitation will be the fins themselves need to fit inside the sabot with ample protection between them and the rifling, this limits the size of the dart even further.
You are also limited by the law.
The ATF has determined that the law states that a .308 is a handgun round I believe, and so using a steel projectile would make it an AP handgun round in violation of federal law.
Making complicated little shapes out of soft metals can give disappointing results. If your thin little fins bend or warp when subject to the stresses of firing because the metal is too soft then they won't do any good.
However if you are using metals that are too hard they may be illegal.
Hard fins also absolutely would need a sabot that is of a thickness that it insures they will never actually touch the rifling, otherwise they may damage it.
However I do not think they consider a 30-06 a handgun round, so you should be in luck.