Yep, broken, specifically with vertex capacities (not edge capacities). I have a little notebook with some of these bugs. It's been sent to WRI more than once.

Another bug is that when we request the OptimumFlowData, then certain documented properties cannot be retrieved.

SeedRandom[42]
g = RandomGraph[{10, 20}]
fd = FindMaximumFlow[g, 1, 10, "OptimumFlowData"]

Now fd["FlowTable"] and fd["ResidualGraph"] don't work. Retrieving multiple properties also doesn't work, despite being documented: fd[{"CostValue", "EdgeList"}].

Some of these problems actually show in the documentation notebooks. You can also check online, just open Scope, and you'll see the bugs immediately in the Out[] cells. https://reference.wolfram.com/language/ref/OptimumFlowData.html

There was a recent Twitch stream dealing with Graph stuff, and you can see bug counts mentioned in the meeting notebooks. It sounded as if there were a new drive to eliminate some of these bugs.