I don't make red velvet because of the red food dye.
In absolute truth, the only difference between a chocolate cake and a red velvet cake is 1 ounce red food dye. Red velvet cake was introduced by the Adams Extract company to sell their vanilla, imitation butter, and red food dye. The original recipe was on the back of their product package.
Since red velvet is just dyed chocolate cake, you can use any GF almond flour chocolate cupcake recipe and add red food dye to make it a red velvet cupcake.
Here's a link to Adams Extract Red Velvet original recipe. You can see it's just a dyed chocolate cake.
Interestingly, the original is not even a velvet cake, it's just a plain chocolate cake with a crap load of red food dye. Red food dye is made from the insect cochineals, so it's not vegan or vegetarian. And since it's a bug, it can cause allergic reactions, including anaphylactic shock.
A lot of vegan and veggie lovers use beet powder for red food coloring. But as it can change the taste of whatever you are making, depending on the amount used, it isn't used often.
There are color extracts from plants of all sorts as well, but they can be expensive.
And yes, Red Velvet cake is just chocolate cake with food coloring in it. Actually, most of the bakeries I worked in used German Chocolate cake batter with red food coloring, as you don't require as much coloring on a lighter chocolate cake, but still get the chocolate taste.
The misleading name "Velvet" relates strictly to the color of the cake with the red coloring in it, not the texture or sophisticated recipe (even though its just choc cake with coloring). This is also the same for Blue Velvet Cake, Blue Suede Cake, or any other "velvet" or "suede" cake.
If you are going vegan, you might look at carob. I know chocolate is vegetable, but carob is slightly better for you than chocolate and to me, tastes better. You also need less sugar and less food coloring for carob....even though it tastes chocolatey, it isn't chocolate heavy.
Here are some interesting thoughts on making your own vegan food coloring....