With cloud sync
Install ShowCards on the new phone and sign in with the same account you used before, your Apple ID on iPhone, your Google account on Android. Your cards download automatically on first launch; give it a minute on slow connections.
Without cloud sync
Create an encrypted export file on the old phone, move it over (AirDrop is easiest), then open it on the new phone and enter your passphrase. ShowCards adds the cards from the file to the wallet.
If both phones have the app to hand, Transfer cards is quicker still: it moves everything over a QR code, with the choice to skip or replace duplicates. See Transfer your wallet to another phone.