Fire Extinguisher can keep everything pretty healthy from a Flamer attack, and allow you to get away, unlike Chem if you're caught by surprise.
Fire extinguishers are useless when it comes to flamethrowers. All they do is briefly extend the life of your components. If you're getting flamed and your crew have extinguishers you have two options: kill them in the next few seconds or rely on superior maneuverability to avoid fire. Otherwise both engineers will be forced to tank which is a losing situation. Getting away from a flame isn't easy because of the ridiculous arcs and range it has.
Right after extinguishing a component it will immediately light up again which gives you two options: mallet or extinguisher. Either one guarantees the component will die if you don't stop getting flamed. More importantly it means that you will be forced to stick on that one component. With chem you can chem the important component then move to the others.
There's no such thing as fighting fires with an extinguisher. It's called briefly extending your life. Chem is far superior because even if you are surprised and get some fires, you can prevent any more fires from piling on. A few fires doesn't do much damage, the main problem is the tool cooldown and the possibility of accumulating more fires. If you chem before a component dies then you bought your ship lots of time for when it gets rebuilt.
I think the extinguisher needs a buff in order for it to be close to viable on most ships. 2 second cooldown with 5 second immunity sounds fair to me.
