Reusing view field formatting?
The best way to do this is by using a display mode for the content you are trying to display. The whole purpose of display modes is to provide a way to render content in a consistent way across the site. 

The field format for views is meant to provide granular control over the content displayed for that specific view. The best way to clone field formatting is to just clone the whole view and modify it from there; however, the first method is definitely the right way to do this.

[Edit] You can use the Entity View Modes module to create custom displays. Once the display is created, you can manage it from the "Manage Display" tab on the content type. If you need further customization to your display, Entity View Modes allows you to provide a custom template for each view mode.