To me, the definitive guide to all these gelling agents is "Texture", the free e-book at khymos.org (which I know about because of this site, by the way). It says that mango is an inhibitor to the working of gelatin, so gelatin won't help as much as you might hope. Having said that, some of the example recipes do use gelatin, so it might still help enough.
About guar gum, it says that acidity (low pH) is an inhibitor; are there any acids in your mango puree? It also says that guar gum leads to high viscosity when warm and low when colder, so cooling it down should definitely make things more solid. You could also try some of the other agents; maybe xanthan gum will help.
If the recipe calls for oil, butter, or any other fat, then you can try to scale the other quantities to match it.
If not, there's still a chance you can salvage it. The oil doesn't actually chemically react with the mix at all, it just "coats" it; in fact, most cake recipes use some amount of fat in order to slow gluten formation (i.e. stop the cake from getting tough and chewy).
However, if the recipe called for 1 1/4 cups water and you used the same quantity of oil instead, then that is going to be way too much oil for a single serving.
What I would do is double or maybe even triple the cake mix, make sure it's very well mixed with the oil, then add however much water you needed in the first place.
If you realized your mistake early (i.e. if the original recipe called for a lot more than 1 1/4 cups of water) then you might be able to just proceed as normal and end up with a very moist cake, but more likely you'll still need to add some more cake mix (and the corresponding amount of water) to compensate. I'd still double it, because otherwise you'll be stuck trying to figure out how to use the leftover mix.
Don't just add flour; the amount of water that the recipe calls for is proportional to all of the other ingredients in the mix, and it's virtually impossible for you to know how much extra water you'll need to compensate for the added flour. Besides, you'd only end up with a bland, flavourless cake if you did that.
If none of these options appeal to you then I'm afraid it's destined for the trash, unless you want to prepare your own cake mix from scratch and combine the two recipes.
Best Answer
I'm going to ignore the actual icing ingredients for a moment here as I suspect they will be mostly icing sugar and a few neglible other things.
So you now have roughly
-> The egg means you need a heating step to get that mixture safe.
If we ignore the sugar, we are looking at a basic pudding mix, albeit with somewhat skewed proportions. So some minor adjustments are in order:
Heat slowly on the stove, stirring constantly until the mixture thickens.
You'll get some version of pastry cream / pudding. It will probably be somewhat floury and very, very sweet, but at least safe and basically edible.
Once you have the pudding, you can use it as a base for desserts, cake fillings etc., mixing with fruit or stretching it with yogurt could tone down the excessive sweetness.
You can also use the thick pudding for a custard-based buttercream, which means you finally turn your mishap into a frosting again.
1 The math, very rough numbers as I don't have the exact amounts you used:
1 tbsp starch / flour ~ 10 g
For pudding, you'd use 20 g / 2 tbsp per 250 ml / 1 cup.
So if your guestimate is correct, use 3 cups milk in total.
For a somewhat thicker pudding, use 30g / 3 tbsp per 250 ml / 1 cup.