Nicolas,
If this were a traditional woodwind, I'd say get a high school band book and learn from there because it will teach you the fingerings. You can probably do that for some Sylphyo fingering patterns, but I think there are enough differences you may get frustrated.
There is a series of method books for clarinet called the Lazarus Method. That's one option. Just use the fingering chart of your choice from the Sylphyo manual and work your way through the book. It's full of easy and challenging exercises and classical/opera pieces that, although intened for clarinet, aren't really instrument specific for the most part. Just bear in mind the book is intended for a Bb instrument, so you might want to set the sylphyo to transpose. That said, you probably have never heard any of the pieces in the method, so playing in any key probably doesn't make much difference.
the method is a series of three substantial books, and you probably don't need any but the first, but thre are a lot of fun pieces in books 2 and 3.