Joey activates Decree, Yugi then chains Fairy Wind. Would Fairy Wind resolve and destroy decree or would it still be negated?

chains go backwards I know but it's still weird to me.

?2015-10-20T09:21:14Z

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As you know, cards activate and then resolve in two steps, and activations can be chained together, resolving in reverse order. They don't have any effect until they resolve, that's why things can be negated.
So,

Chain link 1 - Royal Decree activated.
Chain link 2 - Fairy Wind activated.

Royal Decree does nothing until it resolves.

Chain link 2 resolves, all face-up spell/trap cards, including Royal Decree, dealing whatever amount of damage is appropriate based on what was destroyed.
Chain link 1 would try to resolve. Merely destroying a card does NOT stop its effect from resolving, except in the case of any continuous card, which must remain on the field for any of its effect to be able to resolve. Since Royal Decree has been destroyed and has left the field, Chain link 1 will fail to resolve, it will do nothing.