Linen is a fabric that despite being very soft, has a lot of body and needs a firm filler to properly stuff the fabric.
That doesn't mean that you should stuff it so much that it looks like a "blood sausage" but if you leave it empty it will look much less.
Ideally, you should buy zippered fillings that you can take out or put the fiber inside and if you want to spend a little more money, a feather touch filling, it will give more category to your cushion.
Personally, I am not in favor of animal feather fillings. Ask us about our feather touch fillings and we will inform you.