Did recent bot attack harm my Mac?

My computer was working fine until yesterday, when in the midst of the recent cyberattacks it suddenly started flashing the folder icon and making a clicking noise. I know this suggests a waning hard drive, but I was wondering if my machine had somehow gotten infected and the hackers were using it as a bit? Is this feasible?

In a word, "no." But it does sound like your hard drive is about to die. Check your backups.

The attack that happened yesterday was a DDoS (Distributed Denial of Service) attack against a couple of specific targets, Dyn and L3. Both of these companies provide DNS (Domain Name Service) resolution services to many large companies like Amazon, Spotify, Twitter, and so on. So while those companies weren't directly affected, people couldn't connect to them since using the URL twitter.com didn't resolve to the IP address necessary to make the connection.

Additionally, DDoS in the past have usually been done with hijacked computers working in concert with other hijacked computers. This time around, a piece of malware was used to identify and use IoT (Internet of Things) devices to launch the attack.

Back in the day when people bought routers for their homes, they seldom changed the default password and that allows people to get onto your network and steal data or just your Internet bandwidth for illicit actions. Eventually people got smart about this and the router manufacturers forced you to change the default information.

The IoT devices are going through a similar start where people are just plugging these devices to the Internet and not realizing that they are opening these devices up for hacks..

All that said...in your case, as Jake said your HDD is failing or failed if you seeing the flashing folder image.