So ameraucanas do not have ear muffs, auracanas do. Muffs and beard is dominate, the offspring would have them for a few generations. Anything mixed with the ameraucanas (roo or hen) would produce muffs and beard.
If you do any rooster over a barred or cuckoo hen then it will produce sex link chicks. So the AM (roo) x BR (hen) would be sex link. I actually have a black ameraucana roo x cuckoo maran hen chick, it would look similar to the AM X BR. The female babies of AM (roo) x BR (hen) would be black and males barred.
If you do BR (roo)x AM (hen) I believe both genders are barred. They wouldn’t be sex link.