Your chicks wouldn't be speckled with the first cross. Mottling is recessive so it needs two copies. First cross will give chicks one copy. Second cross will give you some that are mottled and some that aren't.
The pattern you're talking about has different names depending on breed sometimes and can be made in different ways with slight differences. It is kinda a complexed pattern.
I'm working with Wheaton but had Wheaton/ partridge/ wild type mixed in the beganing. It can be buff or red. You need to figure out exactly what you want to figure out what to breed towards.
Find a bird that you like that is a breed so you can look into all the genes it has going on.
I'm working with a mille fluer pattern. Its wheaton, columbian, mottled and I'm trying to split it to two patterns. One buff like the MF and one red like a speckled Sussex.
Buff has different things going on that no one really understands completely. Red is pretty much the same story.
Your project will be challenging because you have several genes that you need to get two copies of all on the same bird.
You'll be breeding to get two of thesw, two of those, two of that, two of this that and the other. When trying to get that many of the right genes on one bird will take a ton of hatching and luck.