The flavor profiles will be similar between these two grapes being black fruit and spice. The Malbec generally tends toward Black Cherries, Plums and Spice (allspice, nutmeg and mace) while the Zinfandel will show more Blackberries, Jam and spice (cinnamon, clove, black pepper and licorice).
Both wines can be full body and can tend toward the higher alcohol levels. California is your go-to for Zinfandel and while Malbec originated as a blending grape in Bordeaux, today's go-to is Argentina.
When pairing, the rule of thumb is to follow WTF...... No, weight, flavor and texture.
Zinfandel can be medium to very-full bodied and Malbec will be full to very-full bodied which gives a few more options for Zin. Malbecs texture tends to be rich, round, silky, smooth, soft and velvety. Zinfandel is chewy, dense, rich, juicy, ripe and smooth.
I would pair Zinfandel with barbeque and grilled meats. Malbec, I would pair with lamb, roasted, braised or stewed beef.
Don't be afraid to explore different producers and always taste before deciding. When you find a style you enjoy the turn to the label for the region and any notes from the winemaker. Use these characteristics as a starting point when looking for another wine you might enjoy. Zins from Lodi will be very similar and you will be able to compare the differences between producers. Zins from Napa or Sonoma will show very different profiles and you can then compare regional impacts on the grape.
Enjoy, and never stop exploring.