I have not read any peer reviewed source that indicates tetracycline is safe to give orally to cats. A buffered form may be given by vets IM or IV and can be useful for certain infections.
Tetracycline given the proper route can cause some very serious issues, so it is always used with caution. Cats are very sensitive to a wide variety of drugs, so I would not risk giving them any drugs without veterinary guidance.
I know this is an old post and the problem has likely resolved by this time, but if others are looking at this thread thinking they can give duramycin, I hope they think twice and decide not to. If a cat is sick, it needs to be evaluated by a vet. If there are monetary concerns, the vet should be able to help you choose an affordable method of care that is best for you and the cat.
Also, note: tetracycline can be toxic to pregnant women, as well as a range of other people. There is a reason antibiotics are controlled by doctors and prescriptions, and it is a very good reason. Tetracyclines can cause kidney and liver damage, and calcium issues (in bones and teeth). Please, please see a doctor if you are sick to get appropriate antibiotics.
One last note: cats cannot have many NSAIDs, including Tylenol and Advil because they are not able to metabolize the drug. Humans are able to, but that does not mean their use is benign. Overuse of NSAIDs can have detrimental effects on the kidneys and gut.
A good source for reading more about tetracyclines: