The short answer is you can't - the borders are controlled through the map layers pane which is basically just an on/off switch.
I'm thinking if you REALLY wanted to create your own map layer file or a data layer you might be able to control it that way but you are getting into some pretty technical and largely undocumented (but it is findable) back-end programming in order to do that - time to ask is the juice worth the squeeze ?
I think you'd have to create a dual axis, which will sort of layer 2 maps on top of each other.
On the first axis, have your regular zip code field on the level of detail with black borders. On the second axis (the one layered on top), create a zip code field that contains ONLY the zip code that should be colored in red. You can then set this border to be red. Example workbook is attached.
A few notes:
When you create the calculated field for the red zip code, you need to right-click it in the left pane and set its Geographic Role to Postal Code:
If you want the zip codes to have borders without be colored in, Set the color to 0% Opacity:
Red Zip Code.twbx 361.7 KB