Do I need a license or certificate to practice chemistry or what are the advantages if did have one?
Note that being a chemist doesn't require any kind of state license or the like in Germany, neither. 

But buying dangerous* substances and running a chemical lab requires that you** have certain licenses and implement safety standards. 
Some of these exams a chemist has to pass during studies (e.g. on toxicology and chemical substances legislation) so having a Master/Diplom in chemistry automatically means that you have those licenses.

Having this license (Chemikaliensachkunde) and being reliable (legal meaning) and of age are legal requirements you must meet in order to be allowed to buy dangerous substances. In practice however, the suppliers put another very practical additional need: they usually do mail orders only B2B and require you to have VAT/USt number.
So if I as a small-scale freelancer who fulfills all the legal requirements want to buy from say, Sigma, I don't get anything because I don't have the tax number (for my size of side-business it would be too much hassle to go through this, so I use the small business exemtion law and for the supplier it would be too much hassle to make sure the buyer fulfills the legal requirements if it isn't at least a certain business size). 

As a private person, you can buy chemicals:


at the pharmacy
at specialized stores, e.g. 

photography chemicals at a good photography stores 
carbide at a speleology outfitter's 
gases (possibly including dry ice) at a gas merchant's, etc.

you basically cannot buy dangerous substances by mail/online order (too much burocratic hassle: the seller would need to make sure of your identity and Chemikaliensachkunde etc.) 
I've never tried to buy privately anything that requires the Chemikaliensachkunde e.g. at a pharmacy so I cannot tell how difficult that is in practice. 


* As a rule of thumb, there are restrictions for substances (or mixtures) that are extremely flammable, oxidizing, toxic or very toxic, (suspected of being) carcinogenic, mutagenic or teratogenic (plus a bunch of listed things)

** or some employee of yours



However, you can of course work as a chemist without (much or even any) need to handle dangerous substances. For example, I'm analytical chemist / spectroscopist / chemometrician. About 90 % of my work is in front of a computer analysing measurement data, developing improved ways of doing so and writing reports/papers. At least half of the rest is in front of a computer programming instruments. I've handled exactly one dangerous substance according to chemicals legislation at two days (actually a sample of few μg I got for analysis) during the last year. The everyday stuff I handle (methanol, ethanol, isopropanol, disinfectant solution and cyclo-hexane and paracetamol=acetaminophen as calibration standards) are not legally restricted dangerous chemicals.
I do handle biohazard material far more often - but that is not what the Chemikaliensachkunde is good for. So for my work, the more relevant safety issues are biological/human material safety and laser safety... It would be quite easy not to have any chemical lab exposure (is seldom enough as it is... - but hey, what did I become chemist for?)

Also I have some colleagues doing the same type of work who are not chemists but e.g. physicists and thus do not have the Chemikaliensachkunde. 



For getting a job it is obviously of advantage if you can show some kind of education/training that makes you fit for the job. For jobs in chemical industry/academia that is obviously a chemistry degree or training as chemical lab technician, but also related professions such as physics/biology/pharmacy/toxicology depending on what the job in question is.