While the East River is paddleable, however it is going to be a real adventure or challenge. If it was flooding it would be deep enough throughout the length however due to strainers and culverts it would be very dangerous. Find a map of the East River here: https://www.google.com/maps/d/u/0/edit?mid=1_nWdwthOhdDP2dd49rbC_lZG_QrAUlc&usp=sharing.
There are no gauges on the East River. The nearest gauge that might provide some insight is on the East Fork of the One Hundred and Two River: https://waterdata.usgs.gov/nwis/inventory?agency_code=USGS&site_no=06819185. When the East River was scouted as being paddleable the gauge listed above was reporting 1.7 cubic feet per second.
There are no designated access points on the East River. The only relatively easily accessible spot is where it passes under 130th St/Cty Rd J20. And that spot is fairly precarious due to the structure of the underpass and riprap down stream. All other access opportunities are at bridges Where you will have to pass down through tall, thick flora in ditches and along the stream bank.
Immediately below where the East River crosses 130th St/Cty Rd J20 Southeast of Lenox in Taylor County the river is 4-6′ wide and about 1 foot deep at the flow rate listed above. The structure passing under this rode is made of two approximately 6 foot square shaped cement culverts.
At 140th Street the River had widened to 6-8′ wide.
At 150th Street while the cut of the river is wide the channel that would be floatable is nearly too narrow for a boat. On top of this there are large downed logs up and down river of the road.
At Utah Ave, there is a lot of riprap that the river flows over both up and down river of the bridge. At the flow rate above it would not be floatable and would be difficult and dangerous to walk through. The riprap along the banks would make portaging difficult as well. Upriver of the riprap there is an accumulation of natural material creating a dam making the depth upriver quite deep relative to the river generally. Shortly downriver there are three obstacles including depth, channels, strainers, and logs. This is a section that could be paddled at a flow rate much higher allowing enough draft over the riprap and obstacles.
At Tennessee Ave. again there is riprap upriver, under, and downriver of the bridge.
The East River meets the East Fork of the One Hundred and Two River just down river of Sherwood Ave. Riprap starts at the Sherwood Ave. bridge and continues to the confluence of the two waterways. While there is sufficient depth for paddling low draft boats at the flow rate observed it will require navigation.