Well, after writing this question, I have come to realize I need it to be truly unique so generating my own might be the way to go. It might not be so bad either. Also, I don't know anything about MAC addresses or how to access them.
You can also read the MAC address using your home router. Just connect your MKR1010 with a sketch to your WiFi network and then have a look in the menu of your router. Every router is different look for pages that contain all connected devices and click on them. They usually tell you the IP address (can change) and the MAC address.
The MAC addresses of your NINA modules are unique. No need for you to generate a unique number yourself. They need to be unique because they are used in the Medium Access Control protocol (part of the data link layer see OSI model) of your network to identify the module in the network. And because nobody knows which devices could end up in a network together manufacturers of network electronics get MAC address blocks allocated by IEEE. So, they are pretty much guaranteed to be unique for the next couple of decades.