Ness is a floaty, so teching throws is usually low percent only kind of thing. I'd think DI'ing away and up would allow you to escape fsmash or side b follow ups.
I don't play Kirby, though, so take my advice with a grain of salt and wait for a actual Kirby main to confirm/refute what I said.
Hold up/away and see if you can jump, airdodge, or throw out a N-Air. If Ness's fastest aerial doesn't help, then I don't know what will.
The down throw is basically always a tech chase setup on fastfallers. At surprisingly low percentages floaty characters can jump out or use a quick aerial. Characters with a frame 1 up-B or something similar can pretty much always use that to escape. In my experience most people seem to just try to tech, and aren't aware that it's possible to escape otherwise (it is quite unintuitive since the opponent doesn't get sent very high in the air). I only discovered it even was possible recently.
Ness is one of the characters that can nair out pretty early. I know Jigglypuff can Rest, though I haven't tested thoroughly to see exactly when (it seems to be a pretty specific DI/percentage). Peach can float aerial or float land down smash.
Once they start jumping out, you can do things like turn around->up tilt or jab instead of going for the tech chase. It's also often possible to regrab no DI or DI in, and sometimes possible to regrab DI away.
Lord Cownostril
Just learn to tech with the correct timing. My guess is you're doing it way too early, but you should be able to tell just by watching how long the gap is between when you actually hit the ground and when you input the tech, and then adjusting accordingly.
If you have to, sit the Kirby (or indeed anyone; all they have to do is one move) down for 2 minutes or so and just get him do down throw you until you get a feel for it; the Kirby player might be willing to watch you and point out where you're going wrong too.
If you can't tech the down throw, then every time Kirby grabs you he can "tech chase" you 0 to death (down throw->jab reset until he can down throw->hammer or forward smash). Once you do start teching, it's still hard to get out of if your character has a bad tech roll (like Ness does). Mix up your techs and use some buffered spotdodges or rolls.
