Can spyware be downloaded to iPhone by clicking a link in a message

Mere clicking? No.

Keep the iPhone updated to the latest iOS always and never Jailbreak. That's it.

iOS / iPadOS devices cannot be hacked or infected with Virus / Malware / Spyware if it is updated to the latest iOS/iPadOS unless you have intentionally downloaded spurious software or unauthorized apps directly from the internet and installed them on your device or/and have Jailbroken. 

It (Hacking) also depends on how careful you are in sharing sensitive and valuable information pertaining to your iPhone such as Passcode, Password, etc with your friends and family members.

Be judicious when sharing the device's sensitive and valuable information with friends and family members.

Software cannot bypass the security measures in place outside of the App Store.

Clicking a link can inform the scammer that your email address is valid and any information you provide can be used against you by the scammer.

If you receive a suspicious email or SMS text message that looks like it's supposed to be from Apple, please email it to reportphishing@apple.com. 

▷ Recognize and avoid phishing messages, phony support calls, and other scams.

You described a scam, not a magical portal that bypasses the security measures that Apple has built into your physical device. 🔐