If you want to make Red Pyle starting from pure Ameraucana varieties, I found a list of varieties with photos here:
http://ameraucana.org/Ameraucana Photos
It looks like the Silver ones have the Duckwing pattern. You could get the gold gene from Buff, Brown Red, Wheaten, or Blue Wheaten.
I don't see any variety that is certain to carry Dominant White, but you could try some whites and see.
Also, it's fairly common for Buffs in any breed to have Dominant White, so you could try crossing Buffs with Silvers and see what comes out. If the Buffs do happen to have Dominant White, then Buff + Silver would probably provide at least most of the genes you need to make Red Pyle. I don't know if you could pick out the right red shade from crosses of those parents, or if you would need to cross in something else (like Brown Reds) to get a darker red.
If you can't get Dominant White from any Ameraucana variety, just pick an Easter Egger who has it, or a chicken of any other breed, and keep crossing back to Ameraucanas until you have all the other traits right. I don't think it's linked to any other genes that would matter, so repeated backcrossing should work fine to transfer that one gene.
I've been trying to google to see if the whites are Dominate but most the info is saying they are recessive.
Even if they are recessive white, they could have other white genes too, and you wouldn't know until you tried breeding them.
I don't remember how much you know about chicken genetics, so apologies if you don't need this part:
There are a bunch of genes that make "white" in chickens.
Dominant White turns black into white.
Silver turns gold into white.
Recessive white turns everything into white.
Barring and Mottling add white in particular patterns, too.
A chicken can also have more than one of those genes, or even all of them.
Solid white chickens sometimes have recessive white, and other times they have the genes for solid black and then Dominant White to turn them white.
Any chicken with a red-and-white pattern has a good chance of having Dominant White (this includes the common Red Sexlinks, and White Laced Red chickens, and "Buff Laced" chickens that have white lacing on gold.)