Any and every possible mix has been used, some with more success than
others. The one you describe isn't "milk paint" though, as the term
is known from furniture.
Blood isn't a pigment. It's expensive (i.e. you need a lot to colour
something) and the colour darkens to dark-brown in a season or two,
certainly not barn red. What it does have though is protein to act as
a binder for something else, especially in an alkaline mixture with
Red ochre (iron oxide) is the pigment of choice here. Cheap, and it
can be mined almost anywhere. Mix that into a simple limewash mixture
and you have a coloured distemper that works fine, so long as it's a
porous surface such as stone or wood. Adding other things, including
blood or powdered milk, will improve the durability of the film for
Google should give recipes, or I've probably got some in old
references (but no time just now)
PS - you're in the UK - we didn't have "barn red" in the USA sense.
Our timber was generally only painted black or white.
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