pulling in an image from another section within a matrix loop
I'm not sure what {% for image in craft.assets.kind('image') %} is all about in your code since the image variable isn't being used anywhere.

But here's the basic structure on how you could loop through 3 separate Asset fields in 3 different single sections inside of a Matrix block:

{% for block in entry.homeMatrix %}
    {% if block.type == "homeMatrix" %}

        {% set firstSingle = craft.entries.section('myFirstSection').first() %}
        {% set secondSingle = craft.entries.section('mySecondSection').first() %}
        {% set thirdSingle = craft.entries.section('myThirdSection').first() %}

        {% if firstSingle.myAssetField|length %}
            {% for image in firstSingle.myAssetField %}
                {{ image.url }}
            {% endfor %}
        {% endif %}

        {% if secondSingle.myAssetField|length %}
            {% for image in secondSingle.myAssetField %}
                {{ image.url }}
            {% endfor %}
        {% endif %}

        {% if thirdSingle.myAssetField|length %}
            {% for image in thirdSingle.myAssetField %}
                {{ image.url }}
            {% endfor %}
        {% endif %}

    {% endif %}
{% endfor %}