I can assure you that in modern computing terms the amount of data a FDR captures is tiny. Sure there might be a couple of hundred different parameters but we are talking about logging parameters (yes/no/on/off) and values (time, position, deflection, alt, speed, aoa etc), not amazing detail digital graphics. This data is then read, replayed and analysed by software on the ground. The data is logged as simple text. In the amount of time it took to load this page on pprune (a page which included graphics and special formatting) we could've downloaded a minutes worth of FDR data at least and that's without compression. Let's not forget that two way satellite based telephone communications have been possible for over 10 years and Internet access has also now been possible for a number of years. The amount of bandwidth needed to transport voice data and internet traffic is far greater than that of what an FDR needs.
For comparision, this from Wikipedia: "According to the publisher of the OED, it would take a single person 120 years to type the 59 million words of the OED second edition, 60 years to proofread it, and 540 megabytes to store it electronically"
Therefore:
59,000,000 words = 540Mb
590,000 words = 5.4Mb
590 words = 0.054Mb or approx 54Kb
I can't imagine a FDR churning out more than a couple of hundred average length words per second. Even if it did we're talking about needing the ability to send this data at approx 50Kbps, i.e. last century speeds. Securing the data is a given. The larger airlines have departments responsible for downloading the data and analysing it. Therefore apart from implementing this solution the only issue for airlines is that of a tiny bit of training and the upkeep of servers that can receive this information around the clock.
I can see how in the past there would have been an extreme privacy issue around FDR data but this should be revisited by ICAO and the manufacturers.