This answer assumes you’re using Version 3 of Scrivener. If you’re using an older version, it gets a lot more complicated…
There are two things here:
a) the actual text of the ‘quote pages’, which is a different type of content from the normal ‘Chapters’. Scrivener calls this the document’s Screen Type
b) the way you want those ‘quote pages’ to look when the project is compiled to different formats – in other words their individual [/b]Section Layout[b] in Scrivener terms.
You want to make sure that each ‘quote page’ has its own document in the binder, then you give them their own Section Type. Right-click on one and choose Section Type > Edit. In the dialogue box, make sure Section Type is selected then click on the plus sign to create a new one: call it QuotePage (actually the name doesn’t matter all, they’re only placeholders).
Press OK, then make sure every one of your Quote Page documents has the new section type QuotePage (by right clicking > Section Type > QuotePage).
Next compile and choose your format – doesn’t really matter which one because the process is the same. Click Assign Section Layouts and allocate your section types in the normal way – i.e. click on Chapter and then choose an appropriate Section Layout (e.g. Chapter).
You’ll notice that the list of Section Types now has QuotePage in, so all you have to do is assign the section type Quote Page to a layout which looks the way you want it to look. To make sure that Quote Pages are always on their own page, choose a layout which has Page Break at the top.
If you can find a layout which meets your needs, then that’s it – you’re done.
If there isn’t one that looks appropriate, then you’ll have to create your own – which is easy enough to do.
You do this by going back to the first compilation screen and Duplicate and Edit the compile format. From this screen you’ll be able to edit the layout which is closest to your needs. Again, this is relatively easy to do, but ask if you have difficulty.
This is a quick skim through what you have to do – it’s actually very simple in practice so hopefully it should get you on the right track.