Because Reed's says they have them in stock, I'd grab some. Either round or flat-nosed will be OK in a low recoiling rifle like a Model 14 even if it does have a tubular magazine.
I read on a forum that flat-nosed rounds were really bad because they had a tendency to not cycle through properly and get stuck in the bolt face?
Just look up remingtonsociety .com website and search for the post "shooting .32 Rem FN verus RN in Model 14's: NO!"
Also, Buffalo Arms Flat Nosed .32 Remington rounds on their website have a giant disclaimer in the description that it won't work properly with Model 14 or 141
Search Buffalo Arms website for "32 Remington Loaded Ammo for Remington Model 8 & 81 Rifles Only, 170 Grain Jacketed Flat Nose Box of 20"
These days. Take what you can get. After things loosen up stock deep. Most of us who were through shortages in the past. Stocked up while the getting was good. Then we have those who never learn.
I'm already comfortably stocked up on my own guns and rounds from before the shortage.
My dad is the one who started looking into or asking a lot of this stuff recently. He apparently wanted to go hunting with his 14 but doesn't have a lot of bullets.
I'm just looking into this as something nice to do for him to perk him up a little bit.