In short, this can only be done as you move along the storyline. I don't want to spoil it, so I'll give you a simple answer: be patient and go through the storyline, and only closer to its completion you will be able to ride a flying dinosaur.
And with such a dinosaur, it is easier to connect all Tallnecks. That is, you won't have to suffer with them as in the first part! Moreover, there are Tallnecks, which simply cannot be climbed without a flying dinosaur.
The action game also received a content update.