They absolutely can oxidize things--fluorine is a more powerful oxidizer than oxygen! And if their atmosphere has no oxygen, but you do have lots of sulfuric acid around, there's probably a decent quantity of sulfur dioxide and sulfur trioxide around as well, both of which can also be used as oxidizers.
In fact, sulfuric acid burns in fluorine gas, so you might want to rethink exactly what your atmosphere and biosolvent are going to be composed of. But, if we run with that for now...
There are a large number of different chemosynthesis pathways on Earth; there would likely be a similar diversity of options on a sulfuric acid world with organosilicon life. What you probably have in mind is a process that splits hydrogen from hydrogen sulfide to reduce carbon dioxide into water and methane, leaving behind elemental sulfur. A directly analogous process would not work with silicon substituted for carbon, or even silicon tetrafluoride substituted for carbon dioxide. Silicon-fluorine and silicon-oxygen bonds are both ridiculously strong, and unlike methane, silane does not release energy when formed. It is extremely unstable in a warm oxygen atmosphere, and would be even more so in a fluorine atmosphere!
The best options are going to depend on the local geological details of wherever you want your chemoautotrophs to live, but the most plausible options are in fact oxidative reactions. Geologic sources produce hydrogen sulfide, methane, silane, or just plain H2. Chemoautotrophs then catalyze reactions of these reduced species with abundant sulfates and/or fluorine to produce some combination of additional sulfuric acid, hydrofluoric acid, elemental carbon and silicon, and carbon and silicon tetrafluorides. You might end up with some complex carbonyl fluorides and silicates as well... but, well, that's assuming you can actually keep a fluorine atmosphere around at all, which is, as I said already, doubtful.