I don't think very many people have tried that flush.
Coke in itself is not considered healthy drink, so most health conscious people generally choose other recipes.
I doubt it is important if you have classic or regular.
You may write down the ingredients and compare it.
Should one eat no fat food during all 3 days (no dairy, no nuts etc.), or these can be taken?
I don't think that is important. It is important to be on a low fat diet the day of the flush.
In reality you can do any flush the way you want it. Experimenting with different things helps find the best recipe for yourself.
But the first time you do the flush, you generally try to follow the recipe.