Applying for research funding as an independent researcher?

Having only a MSc (and not doing a PhD) it might be hard to get an official research funding (although, there are many different programs and maybe there is one for someone with your status; especially if in some way you are still affiliated with an university of institute).

Sadly, (as Paul Hiemstra pointed out) there no such thing as a scientific freelancer. Science market is very far from an unregulated, free market (and the supply is higher than demands, so it is not a place for freelancer jobs).

However, there are two options which may make sense to you:

• doing a part-time PhD, or some PhD where you are not expected to be at the univ. all the time; effectively, it may work for you (though, then it will need to be rather at a low-rank univ.; most likely the most important thing is to find a univ. with no to low teaching load + an advisor who does not care (sic!) or one who understands your situation and is willing to participate in such relationship),
• considering crowdfunding - i.e. describing you project on a website and gathering from all interested people (like on Kickstarter); here is a list of sites for crowdfunding in science (then it is not from government).

The biggest obstacle is that you haven't been through a Ph.D. program. Not (just) because of formal qualifications, but also because a Ph.D. program is where one learns how to manage an independent research program. The reason Ph.D. programs are a de facto requirement for research positions is that very few people learn how to do this in a bachelor's or master's program. It's not impossible, but it's certainly rare. (It's already difficult for recent Ph.D.s to get research grants in competition against much more experienced researchers.)

Aside from appropriate research experience, what you need is a formal affiliation with a university. In the U.S., it's called a "soft-money position." This is a position paid for entirely by research grants, without salary or funding from the university. (Soft money is money that depends on outside grants, while hard money is budgeted from the university itself.) If you can get the grants in the first place, it's much easier to get a soft-money position than a regular job, since there's no risk for the university: as long as your grants continue, they can collect overhead to pay for office space, computer and library access, etc., but if your grants end then so does your job. Of course nobody will give you a soft-money position unless they are impressed with your work and think you would be valuable to have around (and would not hurt the department's reputation), but this is a much lower bar than convincing them to spend their own money on you.

A soft-money position is the closest thing I'm aware of to applying for funding as an independent researcher. (It's not completely independent, but about as close as you are likely to come to independence.) However, in the U.S. it would be nearly impossible to get such a position with just a master's degree.

Whether this path is feasible at all depends on your research area, and of course your funding agency's policies. In the U.S. it's pretty common in medical research, but almost unheard of in mathematics (where there is much less funding available). In computer science it's somewhere in between, depending on the specific subfield.

It can be very difficult to get government financing depending on where you reside. For instance, here in Germany, only qualified workers affiliated with a "recognized" institution, such as a university or a government research organization, can apply for grants. Moreover, only PhD-level staff can act as a principal investigator.

So, the basic upshot is that you need to see what the official rules are in the country where you are working. In general, you cannot work around the qualification rules for such programs!