Like totally chronological (starting in the beginning of the world's story events and going on to the future), or in the present-past-future order, or another?
Is there any specific time order better or more advantageous than the others?
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The previous answers are pretty good, contributing my penny.
If you are writing a trilogy, you are talking about a specific set of characters which are time bounded (can exist for a specific period of time it's upto you to make them live in all 3 books and/or show their ancestors-descendants) in other 2 books. If you are depicting same people throughout the series then it should be chronological. (Enough theory lemme give an example)
I am writing a trilogy of a hero Ashk first book depicts as if it is 2020, so I can't stretch story to 2018 in book 2 or 3, cause readers know he is going to make it in 2020(unless you show time travel where he risks his present if he messes up in past, am I giving you clues, sorry for putting thoughts in your mind)
Another possibility Is the story happens to be about hero Ashk in 2020 and ends up with new hero(say Nymeria) rising. This new hero (Nymeria) can have her story in the same time line for book 2, and you can make wonder in book 3 depicting how it all started/blast from past/mystery revelation/any other cool idea and make both of them coexist or however you may please.
To cut it short, if it's about same person chronological timeline should be adhered unless it involves time travel. if it has more than one central character and a very deep mystery or something like that helping you keep the grip over audience alternate timelines can be used.
PS: its your trilogy you can write it whatever the way you want, the motto should be making yourself happy. One should not write to please people, that prevents him from writing to his full potential.
Hope this helps.
It depends entirely on your story and what you are trying to achieve. Certainly, most trilogies and pulp series are chronological, but there are a number that flow between eras. The one thing they all need, though, is something to connect the separate eras/characters/stories together.
One example is Traci Harding's Ancient Future trilogy, which tells a story that, chronologically, goes all over the shop as the protagonist travels through time - however it can be argued that the story progresses linearly.
Other examples include parts of a series that deal with past events relevant to the story. Stephen King's Wizards Glass, part of the Dark Tower series, deals primarily with events in Roland of Gilead's past from when he was 14.
Raymond E Feist plays with this somewhat in Magician, with the duality of Thomas/Ashen-Shugar and their connection through time.
Steven Erikson's Malazan books also play around a bit with this, with the chronological events not matching the order the books were published in (however, his story and world are epic in scale and the published order fills in a lot of context that would be missing if you read it chronologically).
Cloud Atlas also plays around with different era's characters, although I haven't read the book so can't really comment.
There are other examples that I just can't quite remember at the moment, where there are a number of separate stories all joined by a common link - lineage, some artifact etc. Frustratingly, it's on the tip of my tongue (so to speak). I'll see what I can bring myself to remember and edit my answer accordingly.
Lauren's advice is, as always, good. As long as it is clear to the readers what is happening when, and why, you can present it in any way that works. Having something to use as a point of reference, or link between, is vital for this to work successfully, I believe.