is there a way to transfer passwords, credit card data, etc. from Tiny Password app to iCloud keychain?

You would need a Mac computer and a text editor ( not an office tool like Excel or Numbers)

Look at my user tip which will allow you to export and import passwords to iCloud Keychain using Safari

Obviously Keychain needs to be turned on in the Mac,

Keep a copy of the exported file safe somewhere

Copy or share my Keychain passwords using… - Apple Community

if you can get Tiny Password to export its contents in the same or similar format so you can create another CSV file to append to the end of the exported file in text Editor you could import the whole lot back to Safari and thence into Keychain

When you have done delete the files and empty the trash can!!