In some of my blogs, few articles which were published a few years back has gone outdated. So, I was thinking about republishing those articles. Is there a chance of getting red-flagged by google for doing this and if not then what are the best possible ways to do it.
Republishing old articles can't get you red flagged. You only have to remember the fact that the new articles must contain new information and every possible new scoop loop of data that the old article & along with your competitors are missing.
It's not considered as spam. It rather means that you are evolving yourself according to the needs of audience which is good thing and always liked by the search engines. Just remember that your new post must have new content in it.