[c#] A field initializer cannot reference the nonstatic field, method, or property

You need to put that code into the constructor of your class:

private Reminders reminder = new Reminders();
private dynamic defaultReminder;

public YourClass()
{
    defaultReminder = reminder.TimeSpanText[TimeSpan.FromMinutes(15)];
}

The reason is that you can't use one instance variable to initialize another one using a field initializer.