Just so I understand you clearly -
you're wanting to roll your addresses (which are point data) up into the zip code "boundary" (I use parentheses here because zip codes aren't polygons, they're linear routes). You're then wanting to symbolize your zip code areas with some color scheme to indicate the number of responses, say a light blue-to- dark blue color scheme that looks like this:
If I've understood you correctly, you'll need to add the total number of responses per zip code, and then get these results into a new column in your zip code boundary data, say, call this column TotalResponses or something like this.
Once you've done this, when you bring the results into AGO, you'll be able to symbolize on this field, like this (ignore the Shape__Area, I'm just using this dataset as an example)
Does this help?