New document from layer

I guess I'm surprised not to find on the menu, "New Document from Layer."

Right click on layer then choose : Duplicate Layer. From the Destination section choose New from Document drop down list.

You can also use Layer > Duplicate Layer. It is also available from the Layers panel menu.

I have a flattened document.  I want to make selections and create new layers. 

Expanding on the previous replies...

With a selection active, you can use Layer > New > Layer via Copy or the more long-winded Edit > Copy and then Edit > Paste Special > Paste in Place (both methods retain the original absolute position of the content relative to the canvas).

Then select the flattened Background layer and repeat as many times as necessary to create the layers from the base image.

I then want to turn each of these new layers into a separate document.

By @GButch

The Layer > Duplicate command can duplicate to a new document, however, that is unsaved.

You can then select each layer in the layers panel, right-click on a layer name, and select "Export As" to export multiple selected layers to PNG/JPEG/GIF formats. NOTE: Export As will crop the layers to transparency, they will not contain surrounding transparent pixels and will not retain their relative position to the original canvas. One has to use a more convoluted hack to retain the absolute position and canvas size when using Export As.

One can also use Adobe Generator to name and export the layers to files. To retain the original position to the canvas, one has to add a layer mask revealing the entire canvas to avoid cropping to the layer bounds, or use the previously mentioned hack for use with Export As:

https://helpx.adobe.com/photoshop/using/generate-assets-layers.html

Otherwise, you can use File > Export > Layers to Files – which is probably the easiest way, considering the previous options!

File > Export > Layers to files

@GButch in order to use New Document from Layer - you need to create the layer in your original document. What you are asking for is a "New Document from Clipboard".

I would make the selections, build out the layers on the original document, then use the Export>Layers to Files to convert them all to separate files at the same time.