How do I get my iCloud messages

Did you enable iMessages option under iCloud ?

Settings > Tap on your name at top > iCloud > Enable the "Messages" option.

If that option was ever enabled on your older device or earlier, your iCloud messages will get downloaded in sometime (based on how many messages and how much media you had on them).

See How to set up and activate iMessages for iPhone and iPad https://www.imore.com/how-to-activate-imessage-iphone-ipad

Did you get an error when you tried to activate? See If you get an error when trying to activate iMessage or FaceTime https://support.apple.com/en-us/HT201422. 

Also see If you can't send or receive messages on your iPhone, iPad, or iPod touch https://support.apple.com/en-us/HT204065

Use these support options if you need more help.

Get a call from Apple support to help solve your problem using this link https://getsupport.apple.com/?caller=kbase&PGF=PGF63005&category_id=SC0245&symptom_id=23362

Apple ID Support https://support.apple.com/apple-id

Apple Support Twitter https://twitter.com/AppleSupport

Apple ID account security for country-specific and region-specific help

 https://support.apple.com/en-us/HT204169