Is there a way to measure the chlorophyll content of plants (from e.g. leaves) with basic chemistry equipment (at home)?
To measure the total chlorophyll from leaves, probably not, since you need access to methyl isobutyl ether or pyridine.
But you can separate the different pigments in the leaf. From The Naked Scientist: Cut a rectangle 1 cm wide and long enough to stand up in a small jar from a coffee filter. Place your leaf over the top of the strip and roll the coin across the strip about 2 cm from the bottom. Now add a little nail varnish remover to the bottom of your jar, half a cm is plenty. Suspend your strip of paper so the bottom end is sticking a few mm into the acetone. you can hold it up by folding the top end of the strip over forming a hook which will rest over the lip of the jar. Wait a few minutes, with any luck you should see an interesting effect. Try the experiment with a strongly colored leaf like a purple one.