How can I repair a flexible hot water supply hose that is leaking at the nut?

Over tightening a plumbing fixture can be just as bad as under-tightening, as it can damage the threads and prevent a proper seal.

In your case, you should try to fix this first by reconnecting the pipe with a cleaned fitting:

1. Remove the hose.
2. Remove the existing tape completely.
3. Clean the threads on the hose and the fitting with a wire brush.
4. Wrap new silicon plumbers tape around the threads TWICE - no more - too much is not a good thing. This tape isn't to create a seal, it's to ease the turning of the nut.
5. Reconnect until the hose fitting is snug. DO NOT over tighten as this promotes leaking.

If this doesn't work, disconnect the hose and replace with a new wire mesh hose, using the same taping method.

Does flexible = plastic or flexible = braided hose with permanent nut fittings on the ends?

If this is one of those braided type hoses with permanently attached fittings on each end, then they seal with a rubber gasket permanently installed in the nut fitting. The hose itself could be cracked from age or hardened enough that it doesn't engage with the barbs under the swedge collar and can leak there as well.

The hose assembly is cheap, just replace the whole thing.

Flexible plastic is another thing all together. The top has a ball surface that seals when the nut pushes it into the faucet fitting and the lower end has a nut and a compression collar. If the compression collar gets damaged, it can be replaced.

In this case, a gasket in the hose is likely degraded. Replace the entire hose with a new one. For this particular fitting, PTFE (plumbing) tape should not be used, and perhaps could be causing the leaking if it is preventing the hose from seating properly.

I prefer to use the braided hoses over PVC (Never had a rupture). Their problem area is usually the connection to the shut off valve. I have had new hoses to leak due to over tightening or use of Teflon tape (unnecessary). The remedy is to replace questionable and old hoses. Next, remove unnecessary tape. Then, hand tighten with approximately 1/4 turn (or only enough to stop any leaking).

I had to replace my under sink 4 gallon hot water heater after 18 years (6 year warranty), It feeds the sink and two dishwashers, one on either side of the sink. When I was done the two flexible lines that go to the dishwashers had a small leak. Did not want to replace the lines since they were custom installed through the wall in the back and would have been a real chore to do. I thought of calling a plumber but did not want to spend the money. So I did the repair myself. I got #7 rubber "O" rings from Home Depot. Lathered them with silicone and pressed them into the end that was leaking. #7 "O" rings are a tight fit but that is what you want. Here is the tricky part. When reinstalling the line, you will need to torque the fitting down much tighter than you would normally since you will compressing the "O" ring into the area where the original rubber gasket is. Do not remove the original rubber gasket even though at this point it would not work alone. This solved my problem, saved me $40 in new hoses and untold grief removing the dishwashers and hoses and reinstalling.