How can I get access to a developer account given that I am already a Front customer with an existing user acount?

You can create a free developer account on our Developer Portal. 

If you’re an admin in your existing Front instance, you can certainly access the settings that would allow you to perform developer actions like creating apps that use our APIs or plugin or channel features within your existing account. However, we generally recommend you create a separate (and free) developer account so that you can test your integrations in an environment that does not contain your production data. Once you are satisfied with your app, you can port it to your non-developer, production instance by creating an app in that instance and updating your integration to use the production credentials.

Cheers

--Javier