Do you mean the fleshy outer coating, or the hard shells?

A lot of fiber artists are eager to get their hands on the green hulls of walnuts, because they make a great natural dye...

lisascenic, Any of the artists in S.C. I can get them some hulls.
The only thing is that to much tann in the black walnut can harm some plants. A small amount should be okay.
There is another thread on Blk. walnut leaves & limbs for compost.

I meant the hard shell cracked by the walnut cracker before eating.

All members of the walnut family - Juglandaceae - contain juglone, a natural chemical that has allelopathic properties that can prevent or hinder the growth of certain sensitive plants (the tomato family or Solanaceae is very sensitive to this effect). The highest concentrations are contained and emitted by the tree's roots but the chemical is present in all parts of the plant. Typically, a thorough composting operation will negate any allelopathic effects but it may take a significant time for these shells to breakdown and decompose. They do provide for aeration in the pile and that can accelerate the procees.

The good new is that English walnuts (Juglans regia), which are the most common type for eating and cooking, contain much less of this chemical than do black walnuts, Juglans nigra. In addition to walnuts, pecans and hickories have similar allelopathic properties.

Almonds have no negative effects but again, they can take some time to breakdown and decompose. Nut shells make an excellent and rather longlasting mulch - hazel (filbert) shells are very popular in my area for this purpose. Just expect to have a lot of squirrels visiting to clean out any remnants of the nut meat that might remain!!