In short, yes - Fleep is a Slack alternative.
However, there are fundamental differences between the two. First of all, Slack follows the closed, walled-garden model, where you can only communicate with the people in your team. Fleep is an open network. This means that you can communicate with any other Fleep user and belong to several teams with the same account.
Secondly, Fleep interoperates with email, while Slack does not. Fleep's integration with email works in a way where you can send and receive messages with people who are not Fleep users.
Additionally, Fleep has a native Tasks feature for lightweight and contextual task management. Also, Fleep has seen-bys, which show you how far people have read the messages in any conversation. In Slack, you cannot see participation in this way, so you can't tell whether someone has read your message or not by just looking at the message flow.
These are just a few differences between the two. For a more comprehensive overview, take a look at the answers on Quora: What are the key differences between Slack and Fleep?