Can I make a gluten-free version of these muffins by replacing the all-purpose flour with finger millet flour or almond meal or coconut flour?

No it doesn’t work like that . You would have to use xanathan gum. I haven't baked this recipe gluten free and have read that simply substituting the all purpose flour with gluten-free flour would not work especially in baked goods which has to rise, like muffins, cupcakes and cakes. Brownies and cookies should not be that much of a problem to bake gluten-free and can be done without xanathan gum too. Gluten-free and egg free is a lot of trial and error method only. But some of the readers did mention that they tried this recipe gluten-free using rice flour and gluten-free mix (which already has the xanathan gum in it). You may try it at your discretion. I will try to bake a gluten-free version shortly and blog about it soon.