This only happens on a couple of my documents, not all of them.
Select the flashing text, Format, Character, Font Effects Tab, Uncheck Blinking. This would only fix the selection and not necessarily other styles.
So it may be part of the Font Style.
Press F11 for Styles and Formatting, Click in the general area of the flashing text. The side bar, usually on the right, will highlight the text style (possibly Default), right click on it, select Modify, Format, Character, Font Effects Tab, Uncheck Blinking.
The second choice would be more likely if all your text styles (headings, etc) are flashing. Setting the Default propagates to all dependent styles setting all of them to non blinking text.