For xpnative I have:

ttk::style layout fileselector.TEntry {
                Entry.field -sticky nswe -border 0 -children {
                    Entry.fileselector -side right -sticky ns
                    Entry.padding -expand 1 -sticky nswe -children {
                        Entry.textarea -sticky nswe
                    }
                }
            }

To install a custom style/layout on each theme, I use

apply {{} {
    foreach theme [themes] {
        package require ttk::theme::$theme
        style theme setting $theme {
            style layout fileselector.TEntry {
            # here comes the layout
            }
        }
    }

Thank you for the suggestion.  When I use the code above, I am now
seeing the style/layout being assigned to each theme when I query in
the console.  But when I view my widget, it is not behaving as
expected.  I am trying to put a folder image in the far right region
of the entry field.  I see it on the xpnative theme, but no other
theme.

ttk::style element create fileselector image \
  [list $launchimage {active pressed !disabled} \
  $launchpressed {active !disabled} \
  $launchactive ] \
  -width 16 \
  -sticky w

apply {{} {
 foreach theme [ttk::themes] {
   package require ttk::theme::$theme
   ttk::style theme setting $theme {
     ttk::style layout fileselector.TEntry {
       Entry.field -sticky nswe -border 0 -children {
         Entry.fileselector -side right -sticky ns
           Entry.padding -expand 1 -sticky nswe -children {
             Entry.textarea -sticky nswe
           }
         }
      }
    }
  }