"Flaming" doesn't match the meaning of 炎上 because it's typically used in the context of the one delivering the negative comments, as in A flaming B, and always reflects negatively upon A.

炎上 is used when blog posts/tweets, etc. *receive* such comments and typically reflects negatively upon the receiving party (the post/tweet) rather than the ones making the negative comments, such as when the blog post makes fun of victims of a tragedy, for example. "Flaming" may look similiar to 炎上 at first glance, but it's not an appropriate translation.

The typical wording used when a post generates massive negative reactions is outrage or backlash, such as "Rush Limbaugh's criticism of Pope Francis brings plenty of backlash". Or you can simply use what you wrote - triggered a barrage of negative reactions, which is perfectly fine and also frequently used.