Can I track the Cycle time based on the status of the JIRA tickets?

Sure, Typo can help you with it. To have this configured, you need to provide the JIRA status that marks the start and the completion of the coding phase/development phase.

You can send this information to hello@typoapp.io and we will have this setup done in a jiffy.

For further queries, you can pick a convenient slot for a quick meeting using this link.