How can I survey the customers of my clients?

We're a SaaS company providing web and mobile apps for our clients. Their customers use our product, but they don't know we exist as a company. Now that I'm on board as a designer; I would like their feedback and thoughts consistently.

Naturally I would need to loop in our clients for something like this, but does anyone have experience with how to go about surveying in this situation?

I would ideally like to not just have the survey in app, but also the option to send surveys via email.