Reactive Programming is not new, but it is new to most people. It is simply another name for dataflow that has been around since the 1960's. The Reactive Manifesto is just way to describe the best qualities of Dataflow and Reactive Programming.
A functional language is certainly not needed nor is a huge library. I've implemented many dataflow systems. Most of them are more of a collection of helper functions than what most would call a "library." It really depends what type of features you want in the system.
Dataflow is a very "wide" topic. The system could include many nice-to-have features or it could just have the basics. The core of dataflow is that the data controls execution. This is in contrast to "contol-flow" (used in all mainstream languages like C# and Java) where you tell the computer when, where and how to process the data. The most common form of dataflow is the Pipeline model... a series of boxes (or nodes) connected sequentially to one another with links (aka pipes, wires or arcs).
I have just started to examine the libraries available for Java dataflow programming so I can't give you a specific answer right now. It seems that RxJava is current "name-brand" for dataflow in Java so I would start there. In my upcoming book (http://DataflowBook.com) I will devote a whole section to the available dataflow libraries in common languages, including Java.