That doesn't have anything to do with Zotero.

I got a message saying I had malware from a program called Mac cleaner pro (or something to that effect). I did not intentionally install that. I took it to a company that confirmed it had malware. I don’t think it came from Zotero, but the company asked me to investigate if other had problems. I do suspect it was another site.

I can't imagine this is related to Zotero. Just be aware that there are many types of fake "security" or "cleaning" programs for Mac, claiming they will remove viruses, clean up your computer, etc., but actually are malware themselves. Many people unknowingly install these in an attempt to protect their computers, so be very careful when installing anti-virus or other software and make sure to read legitimate reviews or the background on Wikipedia (multiple sources is good) first. (If you don't easily find trustworthy information about it, that's also a clue not to trust it.) As a general rule, if you don't know what it is, don't install it. In fact, although there are some legitimate programs out there for anti-virus, etc., you're probably safer on average with nothing installed on a Mac than guessing at what is safe security software unless you verify it from trusted sources and have a good, specific reason for needing it (most users don't). The worst of these malware programs may do real damage, like encrypting your hard drive to extort money from you to fix it (or something less obvious like keylogging your personal/financial information), while the "best" of them will just be annoying and hard to uninstall.

As for "Flash update" messages, be careful there too, that's also a common scam. It is a good idea to update Flash and other plugins to the latest version, but always do it directly from the trusted developer-- in the case of Flash, that's Adobe. So if you see a message that you need to update Flash, ignore it, then independently go to Adobe's website (it should be the first Google result too, but verify that), and install from there. If you don't need an upgrade there (or if you do, and install it) then you can always safely ignore any other messages you get. (Rarely outdated Flash can have security vulnerabilities, so it's remotely possible that if you clicked 'allow to run anyway' without updating that you got the software because Flash wasn't updated, by allowing the older version to run on that website.)