SUMMARY
The default method for clients to download a Live Connect on Demand (LCoD) agent is to direct to the company VSA server site (i.e., http://mymsp.com/gethelp). If there is a preference to use an alternative web portal to join a LCoD session, then we'll employ a method to grab the LCoD code as an ID and embed it into the URL. This will allow the client to download the LCoD agent easily.
SOLUTION
OPTION #1
In your site's HTML body, it will require placement of an input element:
<input id="myCode" type="text" name="code">
Additionally, it'll require a button element:
<button onClick="window.open('http://msp.org/ARS/v1.0/?id='+document.getElementById('myCode').value);">Connect</button>
The button contains a function window.open which will launch a new window directing to the VSA site (http://msp.org). Since LCoD sits under the the Authorization Request Service directory and it requires a code in order for it to request the appropriate LCoD agent package, it will plug in the ID from the textbox element and result in the full URL string:
http://msp.org/ARS/v1.0/?id=xxxxxxxxx
An example site may look like this:

When the user inputs a valid code and clicks on the Connect button, the user will be brought to the LCoD page and automatically download the LCoD agent.
Note: It would be prudent to provide data validation to ensure the client isn't inputting invalid values. For example, the code will always be 9 numerical digits long. Attempts to submit with alphabetical, special, or blank value should be prevented.
OPTION # 2
Do a DNS table update that would re-direct the URL to the correct site using a URL of your choice instead of the /gethelp site. Basically, forwarding a defined subdomain to another URL and ideally masking it so for example, you would see help.mymsp.org instead of kaseya.mymsp.org/gethelp.
OPTION # 3
Embed HTML code on your own site to have customers put in the ID number.