How has slang afected American children?
Slang affects American children in the same way as it affects all children everywhere. Slang is part of human language, which is always changing and evolving. Every language has slang, just as every language has idiomatic expressions. Children learn how to use the right slang in the same way they learn how to use other words - they hear them used all around them.
Slang is language constructs that are indigenous to a particular geographic area, or a certain group of people. All languages have slang, but American English is probably richest in slang. Differences in American and British slang sometimes cause embarrassing moments. In British slang, to "knock someone up" is to wake them from a nap. That slang expression has a very different meaning in the USA.
Apart from a few borrowed expressions that the Yanks were good enough to share with us, Australian and American slang have almost nothing in common other than that they are written (should the need arise) using the same alphabet. Most Australian slang is uniquely Australian, but may have had some of its origins in English slang.