You are definitely running too many LED's on one 9V battery. At the most one 9V battery can supply 310 maH, or milliamp hours.
Each LED consumes 20 ma, so if you have 15 LED's your 9V battery can run them for one hour. You are running 22 so you take 310/(20*22)=0.7 or 42 minutes, and this does not take into account the 4060 chip. So I suspect you are trying to pull more current out of one 9V battery than it can handle.
There is one solution so you don't have to rewire the whole thing, use two 9V batteries in parallel. This will keep the voltage at 9V and double the lifetime of the batteries.
This is one of the reasons I don't use 9V batteries with model building, they just don't last long. One AA battery has 1300 mah. Which will last quite a bit longer than the 9V.
As for the flickering, the 4060 might be leaking some of it's signal to the rest of the circuit. One way to fix this is with a diode connected to the power side of the 4060 I have seen this before.
Also I have found out that 4060's can't work with more than 4 LED's. So you should be fine there.