There are various reasons why you may want to sync 2 iCloud accounts, for example, to keep contacts synced between a husband's iCloud account and wife's iCloud account.
In this situation, install the app on 1 of your 2 iPhones and make it responsible for syncing the 2 accounts. Then follow these steps:
- Go to your iPhone Settings > Contacts > Accounts > Add Account, and proceed to add the other iCloud account. Enable "Contacts" only and no other services
- Go to Contact Mover > Accounts, and select both iCloud accounts
- Go to Contact Mover > Sync > 2-Way Sync
Once both iCloud accounts are synced, you may want to configure both iPhones with the same iCloud contacts account to make things simpler. To do so, go to your iPhone Settings > Contacts > Accounts, and make sure both iPhones share the same iCloud account with regards to contacts (you can maintain separate iCloud accounts for all other services).