TLDR: It's possible to 3D print silicone-like materials, but you're usually better off casting silicone parts.
For FDM (extrusion type printers) there are several TPE/TPU materials that provide flex, but none that simulate soft/stretchy silicone. Due to the extrusion process, the filament must have sufficient stiffness to prevent buckling in the extruder.
For that reason, extrusion-type printers are limited to high 80-90's Shore A hardness, which is similar to tire/shoe rubber.
In the SLA space, there are several options for low durometer silicone-like materials:
On our Formlabs printers at COVE, we use a Clear resin called Elastic. It's a 50 Shore A hardness, and is quite springy when cured. I like it a lot.It works well for mechanism advance tires, or for pneumatic diaphragms, or quick o-ring samples. We've had luck printing air bladders down to a 0.7mm wall thickness, thin walls are tricky, and dimensional accuracy is not the best.
Stratasys Polyjet technology can approximate the durometer of silicone with their Agilus and Tango material. But neither has the elasticity that silicone is typically known for. It's more stretchy, with a slow rebound. They can approximate rubber overmold or grips.
Both Agilus and Tango come in transparent/amber color and can be colored on the J750/J850 using the multi-material Polyjet technology.
Carbon 3D is printing a medical-grade elastic resin called EPU 41 which is a really neat material. It almost feels like a silicone foam. It only comes in gray. This is great for skin-contact such as bands/soft electronic sensor pads, etc.
Diversified Plastics in Mineapolis has been my go-to for Carbon printing, but the machines have also recently been added to Xometry and Protolabs.
I recently ran across a company called Beamler Additive that's claiming to print in UV-cured silicone, and I'm sure there are more coming every day.
My recommendation: If you need silicone parts FAST, then try one of these printing services, they generally work okay.
If you're making prosthetic adapters, or watch bands, or prototype seals/gaskets, these might work good for you.
But if your geometry requires thin-walls and a lot of flexibility, then I'd recommend printing an SLA mold and casting the parts in silicone. You'll have much better results.
In one week, you could design a mold, print the mold, and cast 40 parts using quick-curing compression mold silicone.