On 3DS you can launch some flashcarts by sending a stage 2 launcher SRL over to the 3DS via this exploit. Even the original R4 assuming you fixed the potential contact issue that cart has with 3DS card slots. (the old method I made for launching flashcarts before I moved to using NTR Launcher) As for NTR Launcher, it won't work via DS Download Play because it requires slot reset which can't be done without ejecting/reinserting the cart. (which you can't do on 3DS/DSi without it causing slot power off unless you had a passme type device)
Also my builds of NTR Launcher won't work in NTR mode as it expects Arm9/Arm7 SCFG registers to be readable/writeable. So even if you got around the slot power cycle issue, it won't operate correctly. There is an old unrelated build similar to NTR Launcher I forget the name of. It's on filetrip and is basically just the cart loader end of NitroHax with the cheat engine/UI stripped. It was never opensourced hence was the reason why I redid that with NTR Launcher.
But yeah you'd need that old ass closed source version from filetrip to use it in pure NTR mode assuming you had a passme device to get around the card slot issue as you'd need to eject/reinsert the cart after you booted into DS Download Play and before you send/launch that version of the cart launcher.
As for the stage 2 launcher method....you may have issues launching newer carts this way. Carts that use spoofed games may not be launchable via this way and while this may also work for DSi's, really old carts like R4 won't be bootable because DSi powers off the slot for those carts. (If they fail to show an icon on home menu at all, then likely slot won't remain initialized when DSi goes into NTR mode for DS Download Play)
You are better off using ntrboothax on that 3DS if you really want to get old DS flashcarts working on it. Going through DS Download Play is a hacky way of doing it. It only really makes sense on DSi maybe....(and only if your only route to downgrading it is via a hard mod)