With InfusionSoft, Leadlinks can be used to subscribe to Follow-Up Sequences only and only those created with the Legacy Builder. This is a limitation set by Infusionsoft, not allowing applications to send a webform via API.
In other words, neither your Legacy webforms nor your Campaign Builder webforms will show up in your Infusionsoft opt-in Integration in Leadlinks, only Legacy sequences:
For similar reasons, it is not possible to use Leadlinks in a broadcast from within Infusionsoft, which is why Infusionsoft will not show in your drop-down menu to the right.
If you found this article helpful you may also want to read this article: InfusionSoft Legacy Campaign Integration for LeadPages (Video Tutorial)
If you have further questions, please file a support ticket. :)