You can send and receive crypto from your existing phone crypto wallets via the Send/Receive functionality.
Additionally if you would like to monitor balance of your BC Vault cryptowallets on your smartphone, you can use so called "Monitor only" wallets. The only thing they need is public address of your wallet.
Example for Android: Crypto Watch Wallet
Example for iOS: Cold Crypto (Coin Tracker)
A direct connection between BC Vault and Smartphones is not possible at this time, although some ideas are being considered, we don't have any fixed timelines for this feature.