It's not possible to print designs from Zeplin directly, but you can download them as images (as PNGs) to your device.
From the Mac app
Drag a screen (or multiple screens) from the grid view, under your project's “Dashboard” tab, to your Desktop or any other folder and this will give you the PNG version.
From the Web app and Windows app
You can download all of the screens within a section or tag.
From a project's section, click on the "..." button and select the "Download all screen images" options from the dropdown.
To download all screens within a tag, first select the tag, right-click on it and choose the "Download all screen images" option there.
You can also right click on a screen and select the “Download Screen” option to save the screen as a PNG.