It's interesting but just banging amazon with "linen shirt upf" didn't do anything good.
But it turned up another subpage of your referenced page.
It has a nice graphic with a distribution of UPF Rating per material, which should give you a rough direction of how big the differences per material are actually.
Which gives a general direction. From what I read linen performs in the regions of cotton regarding UPF.
Now for the real interesting part: I found this Google Books link which gives quite some comprehensive tables.
This picture emerged for me: The material itself is not as important for the UPF rating as the used thickness, dye, weaving technique and color.
But we can clearly see from the table that Indigo has a way higher UPF than Madder and Cochineal. If we extrapolate this (not very scientific) we can assume that with lighter tones there will be worse UPF.