HEY, ANONS, DO YOU WANT TO PLAY PC VISUAL NOVELS ON THE DS AND 3DS?!? THEN I HAVE JUST THE PROGRAM YOU'RE LOOKING FOR!
Back in 2008-2009, someone made a VN program for the DS homebrew scene called VNDS. It's a small little program, still quite rough around the the edges, but, for all intents and purposes, allows one to port and play PC visual novels on their DS systems. And, yes, you can play it on your 3DS, by extension. If that interests you, you can download the program from here:
https://anonfiles.com/xbm8t6Sbxb/VNDS_1.5.3_7z
With VNs already included and ready to play, such as: (https://vndb.org/v?q=&ch=&f=4ovnd)
>Adagio
>Addendum
>Anon's Nice Day
>Ballad of an Evening Butterfly
>Cross†Channel
>Kikokugai: The Cyber Slayer
>Kira -SnowDrop-
>Never7 -the end of infinity-
>OMGWTFOTL
>Plain Song
>Red Shift
>Saya's Song
>Sekien no Inganock
>Shikkoku no Sharnoth
>Sono Hanabira ni Kuchizuke o
>Sono Hanabira ni Kuchizuke o: Watashi no Ouji-sama
>The Best Eroge Game Ever
>The Letter
>The World to Reverse -hallucinate-
>True Remembrance
>Tsukihime
>Wanko to Kurasou
>Yume wo Mita
Note, however, that there is a couple of limitation with the program, such as the fact that none of the FMVs included with any games will ever play, nor will you ever encounter any gameplay outside of the visual novel itself.

However, for those of you that just want the program and no VNs attached, you can download the latest version of the program from here: https://filetrip.net/nds-downloads/applications/download-visual-novel-ds-vnds-1-5-3-f8988.html
If you want to download only a singular visual novel, or see which VNs have be ported, or have converters, you can find them logged at the following links:
https://web.archive.org/web/20141002214135/http://digital-haze.net:80/vndswiki/index.php?title=Planetarian
https://web.archive.org/web/20150414031453/http://digital-haze.net/vndswiki/index.php?title=Category:Complete
https://web.archive.org/web/20211018150537/http://weeaboo.nl/download/
https://mega.nz/folder/KIUhHTTJ#-fcyoeqVRT_vHxNRMdAp-w
Note that some of the download links from the following sites are old as shit (Still linking to Megaupload), or are simply dead.

If you want to port any new VNs, you can find the guide here: https://web.archive.org/web/20141008165108/http://digital-haze.net/vndswiki/index.php?title=Category:Tutorials

If you want to see about restarting development on the project, you can find the source files, and previous builds, located here:
https://www.gamebrew.org/wiki/DS_Visual_Novel_Reader
https://web.archive.org/web/20110902060832/http://www.digital-haze.net:80/vnds.php
https://github.com/BASLQC/vnds/wiki
The Wiki here:
https://web.archive.org/web/20150520053230/http://digital-haze.net/vndswiki/index.php?title=Main_Page
And, the abandoned attempt to port the program to the 3DS:
https://gbatemp.net/threads/w-i-p-vn3ds-visual-novel-interpreter-for-3ds-homebrew.396564/

Hope I just made some Anon's day, and have fun.