This would be a good one to get answered. I am having the same problem.
You can find that information in the fields property of the layer.
Each field will have a domain property associated with it and will look something like this.
{
"name":"Enabled",
"type":"esriFieldTypeSmallInteger",
"alias":"Enabled",
"domain":{
"type":"codedValue",
"name":"EnabledDomain",
"codedValues":[
{
"name":"False",
"code":0
},
{
"name":"True",
"code":1
}
]
}
}