Chirp for Twitter does not collect any information about you, it's really that simple.
Beyond the information Apple provides to developers that you can decide to provide, Chirp uses no third-party analytics frameworks. Chirp logs no information on you and has no interest in doing such. In TestFlight beta builds Chirp may log some information to your device that you can explicitly choose to share (it will not leave your device otherwise). Chirp does not sell or rent your data.
When signing into Chirp, it requests specific permissions from your Twitter account, such as the ability to post a tweet. This is very simply because in order for Chirp to do anything — something as simple as posting a tweet or following someone — Twitter (rightly) requests that you give the client the ability to do these things. Chirp never performs any actions without you clearly requesting it to (such as by tapping a button). This is very simply required in order for the app to function whatsoever.
Not only do I not care about how you use Chirp (aside from if you want a new feature or find a bug), but I simply wouldn't have the resources to store your data even if I wanted to.