When comparing Flock vs Matrix, the Slant community recommends Matrix for most people. In the question“What are the best on-site Slack alternatives?” Matrix is ranked 3rd while Flock is ranked 5th. The most important reason people chose Matrix is:
Matrix is an open standard, defining simple HTTP APIs so that devs can easily write their own clients, bots, bridges or servers. You're not locked into a specific set of implementations.
Specs
Ranked in these QuestionsQuestion Ranking
Pros
Pro Cross-platform
They have apps for Windows, Mac, Chrome, iOS, Android and web interface. And all the chat sessions are always on sync.

Pro Clean and clutter free interface
Pro Cheaper than Slack
It is half the price of Slack and full of nice features like polls, assign to do's, etc.
Pro Very powerful integration APIs
Unlike its rivals, it not only allows you to receive events, but also allows you to push content to it and receive various user action events.
Pro No IT team required for setup
Moving a team or organization to flock does not require any setup from the company's IT team. At max, what might be required would be to whitelist their domain in case the organization's IT team has gotten external domains blocked. You can simply download Flock and invite others in your organization by using their email ids in order to start collaborating. That's all there is in the name of setup.
Pro Free if you don't need the most advanced features
Most of its features are free, even video conferences. But also they have a Pro version with unlimited chat history, Active Directory integration among other things.
Pro Unlimited groups and teams
There is no limit on the number of groups or of group members. Similarly, within a team you can have unlimited members. There is no limit of number of teams too.

Pro Faster than Slack
Flock is offering an app that is faster than Slack.
Pro Highly configurable permissions
For every team, the permissions and restrictions can easily be set over the participating members and the conversations they are having.
Pro Better than slack
Pro Stickers
Posting messages is more fun with them in addition to emojis.
Pro Customisable UI, integrations surface just like native features
There are multiple options like slash commands, message buttons, chat buttons, attachment picker etc., where the integrations can surface inside the native app. This greatly eases the discoverability of a integration, making it really easy for the team members to find and use the integrations.
Pro Built on an open standard
Matrix is an open standard, defining simple HTTP APIs so that devs can easily write their own clients, bots, bridges or servers. You're not locked into a specific set of implementations.
Pro Bridges other networks into a single decentralised network
Matrix has bridges to IRC (freenode, moznet, oftc, snoonet etc), Slack, Gitter, Rocket.Chat, XMPP, SMS, SIP and others. The point is to 'matrix' all the different networks out there into one single decentralised network.
Pro Has an easy to use client called Riot
Riot.im is the easiest way to use Matrix, with great clients for Web, iOS and Android (and Fdroid).
Pro Does not require a centralized server to establish a connection between two users
Matrix is decentralized, there's no one central point that the information goes through and so no once central point of failure or control.
Pro Matrix prioritizes direct messaging with people the same as Slack-style groups
Matrix aims to "provide an analogous ecosystem to email - one where you can communicate with pretty much anyone, without caring what app or server they are using" using a neutral identity system.
Pro Supports different kinds of communication
Matrix is designed to support Instant Messaging, VoIP/WebRTC signalling (voice and video) and Internet of Things communication.
Pro Has an app store for 3rd party integrations & bots
Riot.im includes an app store with integrations for Github, JIRA, Jenkins, Giphy etc - and anyone can add more via Matrix.
Pro Offers choice of clients
Which can be found here.
Pro Maintains full conversation history
Pro Has an active community behind it
Pro Can be integrated with existing communication services
Matrix is designed to support Instant Messaging, VoIP/WebRTC signalling and Internet of Things communication and allows cross-communication between those services. Meaning one person could be using IRC and another Slack for IMs, or one person could be using Skype and another Google Hangouts for videoconferencing.
Pro End-to-end encryption
Matrix features end-to-end encrypted chats which are syncronized accross all your devices.
E2E is implemented in the matrix-js-sdk library and Riot.im client.
Cons
Con No thread feature
Reply command only quotes snippets. There's no implementation to show thread(s) of an initial message.
Con Keys cannot be checked automatically
You cannot automatically check keys of your recipients. Only manually.
