Yes, you can mine on the testnet. This can be useful to test solo-mining and your mining pool software.

For solo-mining, follow this guide:
https://kevacoin.org/tutorial_solo_mining.html

If you want to start a mining pool, there is a reference implementation:
https://kevacoin.org/mining.html

You can use any miners that support Cryptonight R (variant 4) hashing algorithm.

If you want to implement your own mining pool, it is easier to modify from an existing Crypotnight (e.g. Monero) mining pool software. Kevacoin is derived from Bitcoin/Litecoin, so it is not a privacy coin. But its mining interface has been modified so that it is compatible with Cryptonight stratum protocol and miners.