The life span of a zebra finch is usually 8-10 years. In between these years, the coloration of their feathers would change. By observing the colors, you should be able to estimate how old they are.

This information is mainly for those who are getting a finch for the first time. An earlier FinchMe article focused on visually sexing finches, and this also might be of help.
Unlike trees (and even human beings ), zebras do not have ring lines (or wrinkles) by which we can tell their age. And so the only way to tell their age is by their colors. A young zebra finch, whether male or female, exhibit much duller visuals compared to their parents and other older birds. Most zebra youngs also have black spots on their beaks, and these marks will be visible until two to three months after they are hatched. The next stage is sort of their juvenile phase, where the birds grow more feathers and exhibit more colors. This phase usually has a 4 months-to-1 year period, and you can easily categorize birds at this stage. Males will have begin to show patches of colors in their cheeks and black bars in their chests, and both sexes should be showing distinct orange or red beaks. If the female is supposed to come from a line with dominant black or orange colors, traces of these should begin to show already. Otherwise, it would be hard to tell anything from the female’s color other than the black spots on its beak.
Zebras are considered full-fledged adults upon reaching 1 year. By this time, the male is already exhibiting its full coloration. At some point when the birds are already ready for breeding, the males’ beaks would turn dark red and the females’ bright orange. For the whole duration of their adult lives though, it would be very hard to tell their ages. This means you can only track their age by the estimate you have when you got them, plus the number of months or years that they are with you. In any case, if you are really considering breeding finches, make sure that they are already at least 9 months to 1 year under your care.