How can we measure the rate of reaction of EDTA chelation with zinc carbonate?
I think that the reaction will be too fast for you to measure with the tools in a high school lab. I think that you are not measuring the zinc binding to EDTA but instead making a measurement of the dissolution rate of zinc carbonate in an aqueous solution of EDTA.

If you were to want to measure the rate of the binding rate of zinc by EDTA the best way might be to use a radioactive tracer. I would start with radioactive zinc in an anionic EDTA solution. I would bring this into contact with a non-radioactive solution of zinc. I would then keep on pulling out small samples from the mixture and filtering them through an ion exchange resin which is able to remove either the anionic EDTA complex or the cationic form of zinc.

I would use zinc nitrate or some other form of zinc which does not tend to form anionic complexes when in solution.

I know that this experiment has been done as a teaching lab experiment in a nuclear chemistry unit with radioactive europium, but it has a reputation as a difficult experiment to do.

I suggest you read Williams, K.R.; Choppin, G.R., 1974,  J. Inorg. Nucl. Chem., v. 36, no. 8, pp. 1849-1853. This has details of an experiment on the kinetics of metal exchange between EDTA complexes and "free unsolvated metal" for trivalent metals. 

An alternative non radioactive method would be to use stopped flow experiments with a metal senstive indicactor present in the mixture. If we assume that the exchange of zinc between the solution and the indicator is very fast then this method could be of use.

Another method could be to take a solution of the zinc complex of EDTA and then treat it with C13 KCN, you could measure the C13 NMR spectrum again and again if it is a relatively slow process. But I think for you that you will be unable to deal with this problem with the chemcials and tools you have in a school lab. Sorry for having to pour some cold water around.