Have you set it up correctly in the SendEmail() function to send HTML emails?

I believe so:
Public Function SendEmail(MsgTo As String, MsgFrom As String, MsgSubject As String, _
                          MsgBody As String, _
                          Optional MsgReplyTo As String = "", Optional MsgCC As String = "", _
                          Optional MsgBCC As String = "", Optional SendAsHTML As Boolean = True, _
                          Optional Attachment As String = "") As Boolean

From what I am reading, Gmail doesn't allow HTML to be entered in the body of an email. It looks like Rich Text is the closest it will get. Am I missing something?

Do you have this block of code?

        If SendAsHTML Then
            .HTMLBody = MsgBody
        Else
            .TextBody = MsgBody
        End If

Yes

I ran into that issue myself.  It seems that when using VBA to send HTML your HTML code needs to be concatenated as text.
As VBA only allows 25 line continuations, you may need to break up the code into different parts to get around that limitation.

As per the rules I can't post a lot of code, so here is a snippet.

    Footer = "<div class='divider'></div>" & _
             "<div style='background-color:#E6E6E6; padding: 10px;'>" & _
             "<div style='text-align:left;'>" & AgentBlock & "</div>" & _
             "<div style='text-align:left; margin-top:10px;'>" & _
             "<img src='" & FooterLogo & "' alt='Broker Logo' width='150' height='auto'></div>" & _
             "</div>" & _
             "<div style='background-color:#747474; color:white; padding: 10px; font-size: 8pt;'>" & _
             LegalSmallPrint & "</div>" & _
             "</body></html>"

    Body = Header & Navigation & Footer

    ' Send the email
    SendOK = SendEmailWithHostedImage(toEmail, fromEmail, Subject, Body, ReplyToEmail, CCEmail, BCCEmail, True)

Thanks Michael!