Write and use flashbacks sparingly. Flashbacks can be an overused motif similar to the "it was all a dream" or deus ex machina (an abrupt solution to the problem appears out of nowhere) scenarios. An audience will tune out a flashback sequence they have seen a hundred times before.
Reserve the use of flashbacks for the protagonist or for substantial characters in the script. Showing a minor character's back story in a flashback is lazy storytelling when other effective storytelling methods should be deployed. For instance, a thug does not need to be seen in his youth mugging someone when his present day toothless grin, jailhouse tattoo or dishevelled and bruised appearance can communicate all of that.
Ask yourself if a flashback is really necessary. A voiceover or conversational dialogue scene can be used in conjuncture or in place of a flashback to avoid a hackneyed sequence that could distract an audience. A script that contains a disproportionate amount of flashbacks can rob a story of its urgency and make the audience feel that nothing they are seeing is relevant because it all went down in the past.
Set the tone of the story right away and establish flashbacks early on if your script is going to rely heavily on them. Any experienced filmmaker will state the genre, the world and the feel of the story in the first few minutes. The audience must know early on if they are watching a slapstick comedy or a gritty and nonlinear drama as soon as possible. If your script suddenly erupts with flashbacks in the third act when this has not been established to that point you risk alienating your audience and your story may lose its sting. For this reason, if you are to rely on flashbacks frequently, introduce them near the beginning of the script and the audience will then accept them as part of the reality of the film.
Write and use flashbacks to advance the plot or develop a character, especially if the script is going to take the audience on a nonlinear time-out like most flashbacks suggest. If a flashback is used that does not set up a gag or move the plot ahead, it should probably be omitted unless the script is not story-driven and is more experimental or intended as art-house fare.
Surprise your audience with the logic behind your flashback. Used as a reveal, flashbacks have the potential to really astonish the audience. If it fits the story, a flashback can play out powerfully, particularly if it unravels in such a way that the audience is suddenly let in on a secret that was alluded to but never openly stated. In films like "The Sixth Sense" and "The Usual Suspects" flashbacks are frequently used but in both instances there is a shocking reveal behind them that changes the meaning of the story for several characters and rewards the audience for all the time they invested in watching the film. Because those two examples worked hard at building up to the flashback sequences and large payoffs resulted, keep that in mind when writing your script. If you are going to ask your audience to suspend belief, make it worthwhile.
Structure and write your screenplay to play out like reality whenever possible. A lot of our time is spent daydreaming or living in the past and this is, essentially, what a flashback is. If written as such, like having a character recall some vital information after experiencing a trauma, this creates an identifiable situation for the audience and they will accept the flashback easily. In Alfred Hitchcock's film "Frenzy" the killer suddenly recalls leaving some evidence behind with one of his victims and this very human error on his part makes him sympathetic in a darkly humorous way. Many of Hitchcock's mysteries use flashbacks in creative ways. In his film "Stage Fright" one of the narrators of the story lies in an early flashback and creates comical confusion that takes the film on many creative tangents.
Make the flashbacks you write transcend convention. Because flashbacks are so commonly used and hackneyed, maybe you could use them in your script to be ironic and self-serving. This won't work in all instances but if your script is satirical, in a spoof or avant-garde film it can be effective. A good example of this is in Steven Soderbergh's unconventional thriller "The Limey," which is, essentially, one big jumbled flashback. Other great artistic and experimental films like David Lynch's "Mulholland Drive" and Billy Wilder's "Sunset Boulevard" offer fascinating and far-fetched use of flashbacks.
Write a flashback within a flashback. Since every screenplay goes through many rewrites, try out several techniques and omit what does not work at a later stage in the story's development. Since flashbacks are so often grabs for the audience's attention, try out the flashback within a flashback scenario and see if it propels your tale forward with added momentum. Lots of novels and short stories do this sort of thing regularly and scripts based off them frequently do, too. Screenplays like "The Man Who Shot Liberty Valance," "Frankenstein" and "Watchmen" are all from literate sources that juggle such oddball flashback within flashback devices expertly.
Be assertive and experiment. There really are no hard and fast rules for using flashbacks so long as you are prepared to do a lot of rewrites and be critical of your own work. These are all disciplines that any good writer needs to develop.