I recommend to use thevonline tool on the pfylogeny.fr site. It  carries out gblock optimization and phylogenetic reconstruction automatically (or using the advanced option you can manually set up some parameters as well).

http://www.phylogeny.fr/advanced.cgi

I guess it depends what format FastTree accepts. I use Gblocks on command line as part of a pipeline and modify the output file with a custom python script. There might also be available software that would reformat for you, such as EMBOSS seqret.

It might be helpful if you posted an example line of data in the format you currently have and in the format you wish it to be in.