Indulgently means in that soft, allowing way: you let someone have or do what they want, even if it is a little unwise, and you often do it with a kind look rather than a hard rule. A parent may smile indulgently when a small child tells a long, muddled story. A friend may listen indulgently to the same complaint again. It is not a harsh word; it can even sound fond. Though actually, it can also hint that the speaker thinks the other person is being a bit silly, and is choosing not to stop them. That extra shade — warm, and just a little superior — is why it is not a simple copy of kindly.