How tall can a Fig Tree grow in a year ?????

One foot per month is a common growth rate for a potted fig but no where near the most it can grow.  So if you have a 6 month growing season the average fig can easily grow 6 feet.  My in-ground Hardy Chicago routinely shows stems in late May and by September has dozens of stems over 10 feet tall.  My potted figs don't grow that fast.

It will grow 1-15 feet
unpruned healthy tree will grow 1 to 7 feets
pruned healthy tree will grow 7 to15 feets

it depends on tree stored energy and your climate zone :-)

Depends on if its a old tree that you cut back or died back to the ground and has all of those roots from the previous year.  Or if you mean from a small rooted cutting or 6'' start. 

Here in Hawaii a year is a full 365 days of growth.  A rooted cutting in a 10 gallon pot, I get an average of 1ft per month of growth, so 12 feet a year is avg.  Some varieties grow faster, hardy chicago and desertking are my 2 fastest, during the peak of summer they can put on 2ft a month.  Alma and peter's honey are much slower and grow 6 inches a month avg. 

I had a brown turkey that I planted in the ground and it grew from a 1ft tall 1 gal, to 8ft tall by 20 ft wide by 20 ft long in 12 months and produced 700+ figs.