Not really in a traditional shipping sense? Nowhere near as much as Luckypatch. I vibe with a few for various reasons I'll list here:

Nyehctar/Floweyrus/Boneblossom/Pastaflowers (why do they have so many names???)

I just really adore their dynamic so much. Literal sunshine x grumpy ship. Immovable optimist x unstoppable nihilist. Bonegrave AU is great too. However, I may have the controversial headcanon of aroallo Papyrus. Hear me out!! He loves all of his friends so much, it's hard for him to feel something "more". A true relationship anarchist. That + aroace Flowey, I don't see anything romantic happening there. However, it is canon that Flowey spent a lot of time with him so I'm sure he tried to date him at least once.

Flowisk

I don't show it often enough but their friendship means so much to me. They are the only ones who know what it's like having the power to SAVE. They have both done horrible things and are left with the memories but no closure. Frisk is the first person Flowey was able to connect to after so long. However, I really do see them as purely platonic/familial. Like they have issues like Frisk being the younger child that doesn't have to go through the hurt Flowey did. And Frisk is expected to keep Flowey under control despite still being a kid and not having infinite patience for his angst. But they both still care deeply about each other.

Petalflakes (??)

Ok I recently found out this was a thing, even though people were apparently shipping this since the game came out?? And might be why they were swapped in OG Underswap?? Anyway, I think it's a funny crackship. I know irl Temmie has distanced herself from UT Temmie, but I like to think UT Temmie still has moments of clairvoyance where she has meta knowledge. This keeps her spontaneous enough that Flowey can't predict her.

OCs

I do "ship" Flowey with a couple of OCs for character development reasons. One OC I've kind of scrapped and recycled a lot of his concepts for a Revived!Clover AU. The other...

Because im suddenly obsessed with this ship again LMAO.

Have some petalflakes stuff.

Flowey teaching Temmie proper English, of course being a temmie makes that job rather difficult.

Although it’s unknown if Flowey sleep if he does Temmie will act as a pillow wrapping herself around his stem.

Flowey begrudgery giving compliments.