It is hard to do this without really going to someone trained in the correct procedures. You can easily get a few drops of blood from a finger (you can buy diabetic testing kits which will give you a few microlitres of blood safely and steriley - I could even help you with that) but for anything more than a few microlitres you are looking at piercing a vein and that requires training. You may be able to find a BDSM friendly trained phlembologist but you will need to know that you trust them to be safe and sterile and use fresh equipment.

As for keeping it from coagulating, that is a case of using the right equipment and materials. You need an anticoagulant such as EDTA or heparin (for your purposes it really does not matter which you use). Heparin is, I think, more difficult to obtain as it is a dangerous medical drug which could be lethal in the wrong hands (I remember having to be very careful when handling the vials as a cut finger on the broken glass could lead to a dangerous bleed). EDTA may be your better bet as it can be used in solid form. Best bet may be to obtain some purple vacutainer vials which have the EDTA already in them, are sterile and hold about 5 ml of blood. You may be able to get hold of one of them from a supplier online but be very careful of your supplier and be aware that these things have a best before date for a reason. If you manage to acquire a trained, trusted, kink friendly phlembologist then they may be able to sort out all that for you.

I would be very careful how you do all of this. It is very easy to get an infection (especially hepatitis or HIV) or risk damage to your veins when doing this sort of thing.

If you want to only get a few drops, talk to me in private and I can probably help you out.