depends very much on what route you take and how fast you walk. In viewtopic.php?p=1086#1086
I estimate 2 mths Rome to Arles, chop off 2 wks or so from Firenze. Then, say another 2 mths to Santiago. But ymmv.
One way would be to join the Via Francigena at Lucca and walk the Via to Vercelli, from there take the Spur to Arles and the route from Arles to Santiago is one for which you can get the guide book from the CSJ.
With the AVF Guide see below and the CSJ Guide you should be able to get a good idea of the timescale but I would guess at least 4 months.
The Guida - Vademecum dal Gran San Bernardo a Roma (900km)
+ Spur road from Arles-F to Vercelli with 42 and 19 stages View cover
Published July 2003 by the Association Via Francigena
by Adelaide Trezzini