The short answer is that reflowable e-books don't actually have "pages" — they have one long page from beginning to end, and it's the reader that imposes pagination based on font size, spacing, screen size, and all the reader and user settings. So most elements that are dependent on a fixed page with top and bottom margins just sort of disappear on export.
There are a number of ways to force new page starts and manage vertical spacing. An absolute centering top to bottom is difficult because of the 'flexibility' of the pages, but it can be approximated.
There's no short, simple or universal answer; this is formatting that needs to use several "tools" and each needs to be adapted to the material. Here's a very basic starting approach:
- Create a variant body text style and name it something like PageTop or FirstLine. (It should be in a direct hierarchy from your main Body style, to make management easy — that is, based on Body or whatever.)
- Apply it to, obviously, the first line or paragraph on each page.
- In the paragraph's style menu, under Export Tagging, check the Split EPUB box.
- In the EPUB export menu, under General, check the Split Document box and select Based on Paragraph Style Export Tag.
Now, when you export, ID will create a new starting page each time it encounters a "split" paragraph style, and you will be able to force the text to a page top. (The technical reasons are complicated.)
You can now experiment with top spacing for that paragraph to approximate vertically centered spacing. Obviously, that's going to vary with the amount of text and all of the page-sizing settings of the reader. You may want to create 2 or 4 or 10 child variants with varying top spacing to get the result you want throughout the book. (There is a more advanced method that will let you do proportional spacing, but it requires adding CSS export styling to the project... which is not difficult but a whole additional step.)
Learning to do basic CSS styling is essential to getting the best results from EPUB (and through that to Kindle). But the restriction you're working under, reflowable instead of the (not!) simple, (not!) obvious fixed page, is the right one. Fixed page, FXL, is an obsolete and difficult format and not really appropriate for modern e-books.
Work with the above, and come on back if you have further questions. Happy to help. You might find this essay useful: