Belle Isle is pretty flat, but it's a very popular trail so "quiet" is probably not how I would describe it

Pony pasture and Huguenot flat water are probably the most obvious choice for you. I wouldn’t say that it is super quiet, but the park is right by the river and is mostly made up of a dirt/fine gravel path with pretty much no elevation change. If you venture off the main trail it does become significantly less trafficked.

Three Lakes Park and Deep Run Park in Henrico

Especially if you take the Wetlands entrance, I rarely see more than a handful of people. The Reedy Creek trail is usually pretty quiet too, and is pretty much completely flat for most of the way.

Ancarrow's Landing towards the Slave Trail.
Park at Rocket's Landing and walk towards downtown.
On the west end, Tuckahoe Creek Park is a boardwalk over a marshy area. Completely flat.

Tuckahoe Creek Park!

Dutch Gap - https://www.chesterfield.gov/DutchGap

Bryan Park - https://www.rva.gov/parks-recreation/bryan-park

Three Lakes - https://henrico.us/rec/places/three-lakes/

All are pretty flat with paved or gravel paths, lots of woods, and generally quiet. A portion of the Bryan Park path is near 64/95 and it occasionally has events on weekends.

If you feel like heading north of the city, Poor Farm Park just outside of Ashland has a ton of trails. There’s also the old Richmond trolley path which is a pretty unique part of Richmond history and a bunch of other small parks in an around Ashland more generally. Great small town vibes, quiet parks and good food. Perfect for a local day trip!

Came here to recommend Pony Pasture. Very limited/spotty cell service in there, just a heads up! I always drop my location and give a time frame to friends/family before hitting the loop (it’s about 2mi).

Pony Pasture

Dutch Gap has a long gravel loop along the river south & east of town so it is super flat

Malvern Hill is very flat too

Robious Landing is right along the river and relatively flat! There’s one slight hill about halfway through the main trail but if you keep to the inner trail loops, you can avoid it.

Definitely Pony Pasture and the connected Wetlands trails!

Came here to say this, was out there a little bit ago.

Osbourne Landing has a few paved trails next to the river. Easy parking and a clean bathroom in the picnic pavilion.

The gravel path next to the train tracks in JRPS, accessed at Reedy Creek and other entrances, is pretty flat.

>Ancarrow's Landing towards the Slave Trail. Park at Rocket's Landing and walk towards downtown.

I'm not sure if you're suggesting they walk from Rocketts to Anncarrows, but that's a very long walk. Ancarrows is across the river from Rocketts, and is a 3.4 mile walk to get there, all the way across the 14th St bridge, which means an almost 7 mile roundtrip back to the car. Quite a distance for someone with mobility issues, but Anncarrows does have a parking lot.

https://i.imgur.com/LrM89DE.png

Perhaps you're referring to Shiplock Park on Dock St, which has a small network of dirt paths? In which case, OP could park in the parking lot at Shiplock, if it's not full.

Bryan Park, Dorey Park, Echo Lake, Three Lakes, all have wooded trails with varying maintenance levels but all pretty easy, and they all have a nice flat circle around a lake if you don't feel like going into the woods.

Dorey Park in Varina

Echo lake in Glen Allen is a flat 3/4 mile stroll around the lake, water is in view 100% of the walk.

Dutch Gap was going to be my recommendation. You can do as much or as little as you want but it’s about as flat as trails come around here.

I meant it as two separate options. There is a lot more parking at Rockets than at Shiplock.

Second, Dutch Gap. It's a beautiful flat trail with lots of water to see. There's also the reenactment fort right next to the parking which is also fun to explore (but not free unless it's a holiday like Teacher's Appreciation Day).

You can park at the Manchester climbing wall lot and go along the floodwall trail to the slave trail. It's about 2.5 miles to Ancarrow and very flat. There's constant traffic noise but it's not too loud except under the overpasses.

Could be extended by doing the Ancarrow trail loop too, though it's about a 7-8 mile round-trip at that point.

The wetlands! Part of the JRPS, in Richmond city, has views of the water, the wetlands, and is very flat. It has boardwalks, gravel trails, and natural surface trails. It also connects up to pony pasture and hugeunot flatwater relatively easily! I’ve been going for years to get some solidarity, bird watch, and to look for snakes and small critters. I’m always shocked how uncrowded my favorite park in the city is. I will say, It is rather confusing calling a park “the wetlands”, but here we are. I’d also recommend going to the JRPS website and looking at their maps, The city is full trails, mostly running parallel to the river. Unless I’m going to the mountains or the beach, I’d argue that the nature views right in Richmond city can’t be beat.

Rockwood Park in Chesterfield County is nice and paved on a lot of trails. There are different loops and trails are well marked. Pocahontas Park I believe has paved trails as well. Wanted to 2nd or 3rd Bryan Park. Has lots of really nice wide paved trails and is usually sparsely used even on a weekend. Has a lot of nice dirt trails to explore as well plus a decent frisbee golf course. This is one of my favorite parks in Richmond. Obviously parks by the river are prettier, but they are kinda crowded. Maymont is pretty nice and easily accessible. Lots to explore. Looking over this list and what others are commenting, we do have some great parks and are lucky that the riverside of Richmond has been so preserved.

Texas Beach

Appomattox River Trail Park in Southern Chesterfield is flat and along the river. I only saw a couple people the whole time I was in that park. It's a bit farther than 20 min from the city though.

Buttermilk Trail is flat and near water! Lovely walk.

I'd recommend against Bryan Park; very hilly

I have been following this for a couple of years; https://goo.gl/maps/v5n6EJ6MBwXpLN679 It is a list of places to walk, I would suggest reading the reviews and check out the terrain setting in the maps. Everyone else pretty much listed all of these places, but it is all in one link that you can follow if you have a Google Account.
I prefer going to Pony Pasture and walking around Half Moon Beach, quiet area, lots of trees, until the summer when it is warmer, then the road to the west of it along the river is always a beautiful walk with trees every now and then, I used to love it for photography.

Robious Landing

Yes pony pasture was my thought immediately.

Pocahontas has a nice, relatively flat hike around a little lake