I have an old house with a kitchen light switch that only makes the bulb flash and go off. I cleaned all of the connection points but to no avail.

This could be faulty switch or it could be faulty fixture but it sounds like a faulty connection somewhere.

My suggestion would be to first remove the switch from the wall. Take note of all the wiring connections and then replace the switch. Disconnect all the wiring connections and remake them.
If you don't understand what each wire does, post back and describe the wiring . We will try to help you understand the purpose of each.

If that doesn't fix the problem remove the ceiling fixture and do the same thing. Disconnect each connection and remake. Again, if necessary, post a description of the wiring and we will try to guide you.

If remaking all the connections at the switch and at the ceiling doesn't fix the flashing light, the problem is most likely a faulty connection somewhere else in the circuit. Post back and we will guide you through locating it.

For safety, always work with the circuit breaker turned off.