I have a private key for my wallet and also a keystore for it. I want to use it in MEWConnect. Is there a way to get a mnemonic phrase from a private key?
No, a mnemonic is generated using an hd wallet - a hierarchical deterministic wallet. Private keys are "children" of this mnemonic and there can be millions of them, but there's no way to go back to the parent having only a child private key.
You can generate a new mnemonic if you install MetaMask or most of the other Ethereum wallets out there (Status, Coinbase Wallet etc).
I concur with Paul Berg that there is no way to represent a single private key as a mnemonic, with the qualification that there is no STANDARD way which will automatically work with existing wallets or other utilities. If you wanted to create a mnemonic for backup with a custom algorithm you can use the BIP39 word list, which has 2048 words, and manually map bits of your private key to the corresponding word.
2048 equals 2^11 so you need to split up the 256 bits of your private key into 11-bit segments with padding/checksum added to make it a multiple of 11. A good way is to take the sha256 checksum of the private key and append the last 8 bits of it to the private key, so you get 264 bits, which map to 24 words.