I've experienced the same issue. Best guess is the MacOS speech function copies text into memory and then reads it back to the user. However, the Kindle App likely does not (or cannot) distinguish between copying text for accessibility uses such as the speech function and copying text as one might for a copy/paste function. Thus, after only one or two attempts, the copy limit for the text is triggered. The Kindle software engineers either should have tested for this or built in a native text to speech function into the app.
Minor update - there is a workaround using Voice Over. If you select in Kindle App and press Command + Fn + F5, it will start the Voice Over feature which does not appear to trip the copy limit. It's not elegant and is sensitive in that it will stop reading the Kindle text if you click anywhere or anything while its reading but it works.