From the Kovri FAQ:
What is the current state of Kovri?
Kovri is in active development and currently pre-alpha. Kovri is not yet integrated with monero but, in addition to several core features, we are developing a client and core API for monero and other applications to use.
Currently, you can use the Kovri to connect to (and partake in) the I2P network: browse eepsites, connect to IRC, and run client and server tunnels.
Is Kovri usable, partially usable, or recommended to not be used for actual privacy at the moment?
Kovri is usable to the extent of what
./kovri --help has to offer. Kovri currently has no interaction with Monero. With regard to privacy, we have fixed many security issues since inception but we are still in pre-alpha.
There is still much code to cover so don't expect a strong guarantee of anonymity like with Tor or even java I2P. Those projects have 10+ years of research and implementation experience - and we are just getting started.
Feel free to play the role of developer and experiment/play with Kovri but only if not being anonymous doesn't put you in danger - as there is always the risk of possible de-anonymization due to being in pre-alpha (this is not unique to Kovri).