Is it possible to use brushes made for Affinity in Illustrator?

Somewhat.

Most of them are pixel based, so there is a pixel image. Get that pixel image out of Affinity Designer, import it into Illustrator and create a brush. I would assume, they are either pattern brushes or art brushes, so you choose and then make the brush.

The vector based brushes can be created as either art brushes based on shapes or as calligraphy brushes. In Illustrator it is not possible to change size based on drawing speed. But if you use Astute Graphics plugins, I think you can even do that.