How to change default header image dimensions in twentyfourteen child theme?

The is a filter to the custom header function in the twenty fourteen theme. You can use that to add your new sizes. Here is what I use to change the default size.

function wpse_custom_header_setup() {
    add_theme_support( 'custom-header', apply_filters( 'wpse_header_args', array(
        'width'                  => 1460,
        'height'                 => 220,
    ) ) );
}
add_action( 'after_setup_theme', 'wpse_custom_header_setup' );

EDIT

Also set max width of site-header found in lines 847 to 853 accordingly

.site-header {
    max-width: 1460px;
}