I recently got a phone call from a lady who has a sickly child. Her son cannot have dairy, gluten, but products or soy. The cake must also be vegan. She asked if there was anyway I could make a cake with frosting for him. I politely declined saying I have never made a cake excluding all of those things but that I would look into it. I have made gluten free cakes but not sure about the rest. Is this even possible? Assuming making a cake is possible, What would you use for frosting?

 No recipe to offer, but your post stirs a lot of emotions in me.

Baking is a passion, yet I am a celiac, so I cannot eat any gluten. I rarely eat any gluten free baked goods as they are comprised of highly proceeded ingredients, most of which leave a horrible aftertaste. So called cake made without flour, butter, eggs, milk, etc is not cake. Further the so called alternative flours really aren't flours, but starches and ground up beans or rice.  While the bean is healthful, it tastes terrible in pastry application--the aftertaste is enough to gag me. Yesterday I had a buckwheat cake at a  restaurant and tossed it after a couple of bites because of the horrible taste and aftertaste.  Commonly used ingredients like white rice flour, xatham gum, corn starch, tapioca starch, potato starch might be acceptable if they contained some nutritional value, but they don't. 

Gluten free vegan icing is nothing more than oil and powdered sugar.  Many people are under the misguided notion that vegan, gluten free = healthful.  Where many baked goods are concerned, nothing could be further from the truth.  I'm always baffled by those who shun bleached flours, GMO fruits and vegetables, but think nothing of stabbing a fork into a starch cake.  In the years since I was diagnosed, I've come to accept there are somethings I will never eat again.  But reaching acceptance was a long, emotional journey.  The day I started to bake again, knowing I could never eat what I made, was the defining moment for me...coming to acceptance while embracing what I love most.

Even if you can make allergen free cakes/icing, depending on how allergic they are it could still affect them. That is why products that don't contain peanuts usually say "processed in a facility that also processes peanuts." If her child is really sickly, then perhaps pointing her in the direction of a few recipes might help her better.

I had a roommate once who was allergic to garlic. Just the smell was enough to close her throat. Some people are like that with gluten, seafood, peanuts, etc so be careful with orders like that and make sure you tell them that no matter how hard you scrub your utensils/floors, there may be traces of said allergen in the cake.

As for dairy and soy alternatives, there are plenty out there such as rice milk and coconut milk. I use Lactaid and coconut milk for my son. He's not allergic, just lactose intolerant and will hopefully outgrow it soon.

King Arthur makes a gluten-free and soy free flour. I do hear how gluten-free goods are drier than normal stuff. http://www.kingarthurflour.com/shop/items/gluten-free-multi-purpose-flour. Might be worth checking out or directing her to it :)

I have a friend that has severe reactions to gluten, and cannot even have a speck on a utensil. With gluten allergies,  you need to wash and clean EVERYTHING, because even one airborne particle of flour can cause severe harm.  My son's best friend gets anaphylaxis  from anything peanut, and ended up in the hospital after her boyfriend kissed her hours after eating a Snickers bar.  I have baked gluten free and peanut free but aside from one time baking one peanut free cake for a teen with a severe allergy, I will only do special requests for people with sensitivities and not full-blown allergies, and only when I have no other orders for that weekend. That one cake for the kid with impending  anaphylaxis  was so time consuming and stressful.   I conversed with his Mom several times a day, gave her a list of ingredients  for her approval,  bought new pans and utensils specifically for the job, lost $$$ because I turned down more expensive normal cakes since I  refused to do anything other than an allergen specific cake whenever I am working on one, and had her sign a waiver.  It  was just too risky and time consuming to become a habit.  Unless you have a separate kitchen designated to each allergy, the risk of sending someone to the hospital and potential consequences is just not worth the hassle.

My son had a lot of allergies when he was young and I tried like crazy to figure out baked goods for him, but it turned out he didn't care about bread or cake.  The nerve!  Seriously I tried so many recipes, ground my own flours and nothing.  He was wheat free, milk free and egg free.  Thankfully he could do soy.  I came up with good recipes for cookies that he liked but I used silken tofu for the eggs.  For a cake with "frosting", that's a tough order.  I did just see somewhere today that you can make a whipped cream from full fat coconut milk, vanilla and powdered sugar.  That doesn't sound so bad.  You were wise to turn down the order.  I would be a nervous wreck trying to fill that one!  I do feel for the poor kid, but he may not even care about cake and would be happy with a dairy free ice cream or sorbet.