Hello and welcome to the forum
The only natural red dye that takes really well on leather is ironstone.
It's a substantive dye and doesn't need any mordanting.
Madder is good, but unless your skin is very white and clean, free from oil, etc., and you alum it, then the madder will be dark, muted, plumy kind of tones.
The Inuit dyed their boots red using ironstone, but ironstone's very variable. Round here any that I have found tends towards orangey colours, while I know that further north the stone is yellowish or brown toned.
Scarlet red, I don't know. You might try the stuff the Navajo weavers use though, the cactus insects, cochineal….though I found that too ended up pink toned rather than red.
The other thing, since it's skin, and that would be the better for having grease or oil in it, is to try alkanet. It doesn't yield it's dye in water or in alcohol, but it really, really gives it off in oil.
I know the translated Alexis of Piedmont (somewhere around the late 1500's) gives instructions for red, but well, I have my doubts.
I can find you a link to that though.
http://www.personal.utulsa.edu/~marc-carlson/leather/ld.html
"To Die Skinnes in chickweede, called in Latin Rubra Maiore, or Rubra Tinctorum, into a Redde Colour.
Having annointed, washed, wronge and layed abroad the skin, as is aforesaied, wete it with water that white wine lees and baye salt hath ben boiled in, and than wring him. Take than creuiles or crabbe shelles (be they of the sea or of the river) burned into ashes, the whiche yon shall temper with the said water of the lees and salt, and rubbe well the skinne therwith, than washe him well with cleere water, and wringe hym. This done, take ruddle tempered in water of lees, and rubbe the skinne well over and over with it, and than with the foresayde ashes, wasshinge, and wringinge it thre times. Finallye, after you have wasshed him, and wringe him, if you thinke it not be well ynoughe, you shall geue him one dienge with brasyll. The paste or masse of Rubia Tinctorum, must be made with water that lees or tartre hath bene boiled in, and the sayed water must be luke warme, and whan you make the paste of ruddle, than leave it fo the space of a night. After this, put upon the sayd Rubra Tinctorum, a lyttle alom, dragges,or lees, or Alome catinum, steped in water. You maye also adde to it the colour of the shearing of scarlet, whiche hath been taken oute boylinge in lye, which is a goodly secrete."
The last thread we had on this topic was started by a fellow who was a bookbinder looking for information too.
I don't think he visits the forum now, but it might well be worth while seeing if you can get hold of him for advice.
http://www.bushcraftuk.com/forum/showthread.php?t=63556
cheers,
Toddy
