Are you referring to a English or western sized saddle?
Big difference.
I see English...

As for size in English....
A saddle, regardless of how "flat" it is or not...
16" and smaller is for a junior rider, and smaller are child sized in length of flap and where the twist, the deep spot of the saddle is for weight bearing balance made into the saddle.
Unless a petite adult, even then, very few saddles English 16" and smaller are going to fit the physical needs of a adult rider.
Not just length of flap but how it is cut to accommodate the shape of a adults thigh and lower leg thickness.

If this is a western size saddle, then these are adult sized saddles....
🐴....

 

As I said, I ride English and I know what size saddle I can ride in. I've ridden everything between 15.5" and 18" saddles. I can ride in a 15.5" but would prefer a flatter seat for that as I feel safer, and it's unrealistic to look for a 16.5" or bigger for his back as it won't fit. Do you have a brand or style suggestion?

 

What you want and where it will place your weight on the ponies anatomy is what needs recognized...sitting your weight on a cantle is not helping the pony one bit but going to sore them.
And you might fit in but it is not a optimum size for your body and that puts more stresses on the saddle tree, hence to the ponies back..
You riding in a child's saddle then should be what you ride in all the time...instead you gave a huge range of size and construction of said saddles.

Without pictures of said animal no one could suggest...
My wildest guess would be search for a older Prix de Nations saddle cause that is about as flat as you can get that I know of.

Good luck and protect that ponies back by riding in a appropriate sized saddle or...cause you can doesn't mean you should is not what you want to hear but your pony may find that to be true if you sore him from sitting in the wrong spinal location.
Bareback pad to saddle is different where that weight gets placed and how and where your pressure point sitting is felt
Good luck
🐴...

 

I was going to try to offer some suggestions, as I ride a 13.2 Pony with a short back. But now I think I will pass.

 

Thorowgood and Kent & Masters make the same saddle design for ponies. The Thorowgood is made of synthetic or cheaper materials, but is the same design as the K & M.

I can't find the panel measurements online. However, looking at my own saddles, it appears the panel on most saddles is about a half inch to an inch longer than the seat size. My 17 inch saddle has an 18 inch weight bearing area. If your horse truly needs only 16 inches of weight bearing area, then a 15.5 inch saddle is probably the biggest you can go.

As others have said, that only works if your seat can fit in the saddle without putting you on the cantle, based on your thigh length and stirrup length. Otherwise your attempt to not go past the weight bearing area of the back will not help the horse, because your weight will not be balanced on the saddle. I wouldn't say following the rule of saddle length will be more helpful to your horse than having your weight tipping the saddle back.

I have a pony with a very short back and forward girth groove. I decided it would be too difficult to find a saddle that was short enough for her back length and also would stay clear of the shoulder, so I bought a Ghost treeless for her. With some treeless saddles, the panels can go farther back because the weight bearing area is only under the rider's seat. Without tree points, the saddle can also sit farther forward over the shoulder blades.

I have the Torino model.

England has a wide range of saddles made for small ponies, but unfortunately they are harder to find in the US. There is the Native Pony Saddle Co, Chunky Monkey Saddles, and the Pony Saddle Co., should you wish to import a saddle. Adults more commonly ride native ponies and small cobs over there.

 

If you go back and read what @horselovinguy wrote, he did recommend an older Prix des Nations saddle. If you are not familiar with Crosby saddles or the Prix des Nations model, then ask here or google.

 

Many of the older jump saddles or even AP - and by older I mean by 30 or more years have flat seats. New saddles your best bet is a Pegasus.