To know how to breed different shades of grey you need to understand how the dark factor works & also how to produce double factors
Because grey is a colour adding factor, and not a colour in it's own right, the shade will be influenced by the colour that the grey is added to. If grey is added to a sky blue budgie it will be lighter than grey added to a cobalt or a mauve. Also a grey bird that is a double factor is usually darker than a single factor
Slate is a separate mutation so to breed a slate you would need a bird that is carrying the slate gene
Slate is a completely different mutation than grey. You can't breed slates through greys unless they are split for it. Both birds have to be split for that mutation in order to produce slate chicks. It is VERY rare
It is sex linked, and quite rare, so your best bet would be to find a slate male and pair him with a skyblue female. Again, they are very rare, so not likely to be found.
Cobalts have one dark factor, not two. Mauves have two dark factors; skyblues have none.
If you paired your female with a blue male, you would get approximately half blues and half greys. The shades of blue and grey that you get would depend on the male's color and whether your female is sf or df grey, as Nev posted.