No animal ingredients:
100% linen hand-dyed (including LinenNaturals).
100% linen plant dyed.
Flaxi 100% linen.
And of course the undyed 100% linen yarn (natural or soft white)
The Alpalini range is obviously not vegan, since it's 50% alpaca fibre, but you can safely use any of the 100% linen yarns. Some natural dyes are derived from insects (cochineal, lac) but we have never bought or used any of these. Any natural dyes and mordants we use are of plant or mineral origin. Synthetic dyes and washes are not derived from animal ingredients. I am not sure about the wax used on Fil au Chinois linen thread. I would have to contact the company that makes them to check.