For Azure VMs you need two or more VMs in the same availability set before Microsoft will honor the SLA. Does the same thing count for App Service Plans? Do you need to have more than one instance before the service plan is considered "highly available"?
Azure's App Service plans are already highly available, from a service perspective. That is, it's a multi-tenant service set up for high availability, where you don't need to worry about the infrastructure.
SLA-wise, you don't need multiple instances of your Web App. However, the SLA doesn't apply to free/shared tiers. SLA details for App Service are here.
Just keep in mind: If, for some reason, your app needs to be restarted (e.g. app pool recycling or some other reason), you might experience momentary unavailability if you only have a single instance of your web app running.
From a content perspective, your code won't be lost if your web app instance goes down, since code is simply copied from somewhere else. Same goes for your local disk, which is shared amongst your web app instances - it's a durable store (unless you delete the web app, of course).