Whisker Biscuit rests are notorious for chewing up flimsy plastic vanes. There are a few things you can do to fix this problem. First, you can use a stiffer vane. I have tried Norway's Duravanes and Bohning's Blazers. Both are stiff and rugged vanes that will hold up well to the bristles of the Biscuit.
Second, you can use short fletching. Again, this comes back to a fletching such as the Blazer. Short fletchings aren't as likely to be damaged as they pass through the rest as longer fletchings.
Third, you can use straight fletching. This is not my recommendation, but it will reduce damage to the fletching. The only fletching I would consider using straight is the QuikSpin from New Archery Products. These have little tabs built into the trailing edge of the vane that will cause the arrow to spin even if it applied straight, without any helical.
You can also apply a helical offset to short, stiff fletchings such as the Blazer without too much damage to the vanes.
These are the only options I would consider with the Whisker Biscuit. For sure, I would avoid any option that doesn't cause the arrow to spin to stabilize it in flight. You need that arrow spinning, so don't be tempted to use a straight fletch with anything but QuikSpin vanes.