I have an XML file format that I would like to open from Internet
Explorer 6 directly into my client application, with no warning dialog.
So, given an example link:

<a href="http://trusted.company.site/test.kml">Test Link</a>

When I click, it should download the KML file (an XML file with a
proprietary extension) and open it in my client application with no
intervening dialogs. (The client application is already registered to
handle files with extension KML).

Instead, IE seems to determine that since the file is XML, it should
display the XML by itself. (This of course, scares our users because
they don't know anything about XML).

If I set the mime-header for content-disposition, then IE will pass it
off to the registered application properly, but the Open/Save dialog
appears, with no option to set a default (i.e. Do Not Ask Me Again
checkbox is disabled).

We need it to be seemless; a user clicks the link and the document
downloads and opens directly into their desktop application, without
IE intercepting it and displaying the XML or showing warning
downloads. How can we configure IE to do this?

It is acceptable to configure the site as a "trusted site" or "trusted
zone" if that helps with the solution.

This sounds a lot like your client app is somewhat of an RSS feed
reader. It doesn't matter whether the site is trusted or in a trusted
zone.  First let's double check that windows in fact has a file-type
association between the *.kml file type and your client application.

right click start>explore>tools>folder options>file types>scroll down
to where a KML extension would be alphabetically and select that

it should say 
"details for 'kml' extension:
opens with: your client application"

if it does NOT, click change and select your client application,
browse if it's not in the given list

NEXT, you must do the same for the *.XML file type as well since IE
automatically opens that file-type by default by showing code, IE does
not natively read XML, it needs an add on such as an rss reader or
other plug in to properly read it...
anyways do the same for XML and select your client application to open
XML file types as well because sometimes IE goes by the files
composition and assumes it's XML even when it says KML.

please tell me how that goes, if not switch to mozilla firefox, i live by it :) lol

i do understand your situation though

actually go ahead and when your trying to change the opens with
dialog, click advanced (this after the whole right click
start>explore>tools>folder options>file types)  and deselect "confirm
open after download"

and then select the "open" option in the list and "edit" and change
the application that opens the file-type manually by typing in the
client app's location