I know that Mercury is still being included in the flu vaccines where I live because I requested an insert that comes in the box that Dr's/pharmacists get not the one that costumers get if requested.
Hopefully there's options, like what I'm posting below, where everyone lives if you want to get the flu vaccine without mercury.
I get my flu shot at a pediatric/kids clinic. They don't use mercury (thimerosal) in their flu vaccines. They (at least here or at this clinic, hopefully everywhere) don't get the ones that contain mercury for the kid's flu vaccines, maybe it's not in any of their other vaccines too.
You can find out which flu vaccine doesn't have mercury each year and see if your doctor's office or pharmacy carry it too. Or ask them if they carry it (and check it out from there). Generally I've found they carry both kinds (with and without) mercury.
I get the name of the maker, etc and check all the ingredients ahead of time.
There's an official site that lists all the vaccines, makers and all the ingredients.
Some places can run out of the mercury-free (thimerosal-free or preservative-free) so it's best to get it earlier in the season.
https://www.cdc.gov/flu/about/qa/vaxsupply.htm
For the 2017-2018 season, manufacturers will produce influenza vaccines containing thimerosal and some vaccines that do not contain thimerosal.
Approximately 130 million doses of thimerosal-free or preservative-free influenza vaccine will be produced for the 2017-2018 flu season.