It's good advice. Write down the events in the order in which they occur. Keeps the story straight and moving forward, and does a better job keeping things suspenseful.
Then, I have written two stories that opened with the climax and flashed back through the entire story before finishing up with the rest of the climax and denouement.
Sold them, too.
In other stories I haven't use a flashback scene for many a year. But characters do ruminate on the past where relevant and when needed for info-dumping purposes. Which can be dangerous in itself. Especially in the first few pages, where too much past perfect is, in my experience, a warning that here is rather too medias in the res.
There are two different techniques here. One is to do something so strange and dramatic that the readers will want the backstory out of pure curiosity. How strange depends on how long the flashback will take. The purely dramatic will do for a short scene: the princess snubs the courtier because he had insulted her when she was lacking in influence and far from the throne, before a plague took out three quarters of the royal family. But strangeness really helps, especially when it gets long -- like, for instance, my two stories. And even if there are strange, strange, strange things going on, it should be a technique for when you can't tell the story linearly. For both my stories, there was really no way I had a hook in the earlier stuff. At least, not in a situation where I could start the story without backfill right away.
For the rumination, I first consider whether they can talk about it. Since it's important to the story (right? You're not including irrelevant backstory for the heck of it?), it might plausibly come up. Preferably when the characters can get some conflict out it. But not always. The character may be too sagacious to give away what he knows, or that he still remembers, to his enemies. Still, dialog passages are among the best locations to have the character fume and rage and remember why and identify the lies the other character is telling.
But whether in dialog scenes or otherwise, the trick to such little flashbacks is to weave them in. In the same voice as the rest of their thoughts -- preferably a limpidly clear voice, carrying the reader on without any ripples or eddies disturbing the flow. With the memory motivated by current events. And in small enough doses that the reader can read through them without quite noticing that they are flashback.
Because for these flashbacks, transition is the issue even inside a scene. And the time factor is always fun -- how long ago did this occur?