I think the reason people dislike flashbacks is because, when done poorly, they are conveniently placed RIGHT before the information from the flashback is needed in the main plot - even if it made no sense for a character to have a flashback in the moments leading up to it. It's jarring and feels like an author desperately trying to cover up a plot sinkhole that just opened up.
The vast majority of stories feature flashbacks or memories (snobby people will call that kind of narrative "non-linear storytelling" in that case, because gods forbid they use the word "flashback.") If your flashback makes sense within the emotional arc of your story, makes sense with the adjacent present-day scenes, and is ideally set up ahead of when its content is needed, then I don't think you have a reason to worry.
For a webcomic that does flashbacks well, there is Ava's Demon. (It's big enough to be the first link that comes up). I haven't kept up with it in years but I remember that originally there was a lot of, um, "non-linear storytelling".