I'm not in the mood for a lot of math, but I think there are only 12 combinations of these three words in which kid is always used twice and the other two words are used once. I don't really care about that since this is a linguistics post.
The arrangements can be categorized into a few different meanings:
1. An immature goat which is nice to children.
2. An immature goat which is friendly in a general way.
Goat kid, kid friendly 1
Kid goat, kid friendly 1
Goat kid, friendly kid 2
Kid goat, friendly kid 2
Friendly kid, kid goat 2
Friendly kid, goat kid 2
Kid friendly, kid goat 1
Kid friendly, goat kid 1
Kid, kid friendly goat 1
Kid, kid goat, friendly 1
Friendly goat kid, kid 1
Goat, friendly kid, kid --this one may be unintelligible even with helpful commas