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Do you have a 2 wire voltage tester?
One of the black wires is the feed and the others are to the kitchen light and to the breakfast room. With all 3 connected together both lights should work, one without a switch. Put them together and then remove one at a time until the kitchen light goes out. Now check to see if the breakfast light is still on. If not, the wire removed is the hot. Let me know how it goes.
No put them together with a wirenut. You'll need a wirenut for the final connections. Only one wire under a screw and never use the pushback connections.
Hold on. The statement in your question said that you had 3 black wires. What do you have?
Not having a tester to identify the hot wire, you need to put the 3 wires together and by elimination determine which is the hot wire. When together the lights should work. One will not be switched. The wire that when connected to either of the others allowing a light to work is the hot. When you find it we can continue. The alternative is to get a 2 wire tester