Eleni, I'm sorry to see that nobody local to the places you mention has replied, so I'll do what I can from a distance.
It's not entirely clear whether you're looking for eating-out vegan, or ingredients for vegan self-catering.
I am pretty sure you won't find a vegan taverna as such in the whole of Crete. One site I have bookmarked promises vegan/vegetarian restaurants, but the half-dozen listed for Crete are all vegetarian.
But as I'm sure you know, Cretan cuisine offers a number of dishes which are suitable for a vegan diet. This website has some thoughts:http://thegreekvegan.com/
If it's about self-catering, the basic ingredients - the vegetables and fruit and the pulses - are of course readily available and of terrific quality. But when it comes to the specialist ingredients to boost those basics, it's going to be much harder, I think. Before the crisis there was a burgeoning of health food shops which had those ingredients, but all those "luxury" places have been hard hit.
Rethymno used to have two good health food shops selling a lot of specialist-diet items, but both have closed. I don't know what it the situation in Chania, but maybe some else does? And there is a food shop in Kalives called Toko which sells a huge range of gourmet/ethnic/specialist foodstuffs. I haven't been there for ages so I'm not sure how useul that would be, but I'm sure one of the regulars here who live around that way could perhaps ask what they have? Certainly they stock quinoa because we had a thread about it on here.
P.S. Just belatedly thought to look up Toko's website, and I see they offer tofu and soybean products.http://www.tokokreta.eu/EN/index.html