The main strategies for making fake blood that won't stain clothes is either to keep any food colouring suspended in solution so it doesn't set or to come up with an alternative colouring agent. If you do use a dye like food colouring, you'll want to keep it moist so the dye doesn't bind to the fabric.
Combine one cup of light corn syrup with a teaspoon of red Kool Aid powder (cherry), a dash of green or blue Kool Aid powder (lime or berry) and one teaspoon of clear washing powder. Test it on a rag to make sure it doesn't stain. If it does, use more dishwashing detergent. Use washing powder over dish detergent; use hand detergent only as a last resort.
Use Lynx Instinct Shower Gel or dark red dishwashing liquid. Add strawberry syrup or chocolate syrup to the latter for opacity. The Lynx Gel is already the right colour and opacity. The colour washes out when you throw the clothing in the wash. No bleach required. Strawberry and chocolate syrup come out in the wash also.
Mix 200mL of water, 5 tablespoons of corn flour (cornstarch), 300mL of corn syrup, 2 teaspoons of fresh cream (or non-dairy creamer), 5 teaspoons of red Kool Aid powder (cherry) and a pinch of green Kool Aid powder (lime). The cornstarch and cream make the consistency more realistic. The green helps darken it.
The above instructions don't use food colouring. If you do use food colouring and it stains your clothes, soak the stain in a mix of liquid Tide, distilled vinegar and warm water for 20 minutes. Then rinse it out with vinegar, rubbing it in with your fingers or a scrub brush. Spot Shot carpet stain remover may also work. If you do use food colouring, use the powder, not the liquid form. British readers can use golden syrup as an alternative to corn syrup.