Found a workable solution. Create a PHP script on the machine that accepts the variable from the URL then sets it as a Keyboard Maestro Variable using AppleScript:
<?php $myVariable = $_GET["input"]; exec('osascript -e \'tell application "Keyboard Maestro Engine"\' -e \'make variable with properties {name:"VariableName", value:' . $myVariable . '}\' -e \'end tell\''); ?>
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