I've never heard of RR used to increase milk supply. RR tea is generally used in pregnancy to tone the uterus.
The tea is actually made from red raspberry leaves. You have to be careful when buying it because often the Tea is flavored with raspberry and not made with the leaves. It think it is also available in a pill form.
If you are personally having a supply issue, please seek help from your health practitioner &/or a lactation consultant (no herbs are likely to help a low supply if other proper steps are not being taken).
The raspberry leaf is the part of the plant used for supply. As a lactation consultant, the herb I see most frequently used for increasing supply is fenugreek (see link). The following information on raspberry as a galactogogue is from The Nursing Mother's Herbal :
"Safety: Although German Commission E could not identify any risks associated with raspberry leaf, it has not approved its use because no sutdies of efficacy could be found. Regardless, raspberry leaf is extensively used during pregnancy to prepare for labor and breastfeeding. For most women, it is unnecessary to use this or any other herb during pregnancy to make sufficient milk, but prenatal use does not seem to overstimulate supply or contribute to engorgement in the postpartum. Raspberry leaf contains tannins and is thought to be somewhat astringent. It is believed to lower milk supply with long-term use in the postpartum, even though it seems to increase supply when used short-term (less than a week). It is best to use raspberry leaf only briefly and as a minor part of galactogogue recipes. The AHPA labels raspberry leaf Class 1: safe when used appropriately. It notes no restrictions.
Dose: To make tea, combine 1 teaspoon (0.8g) finely chopped dried leaf per 5 oz. (150mL) boiling water; steep for 5 minutes. The tea may become bitter with longer steeping time. Some women consume 1 quart of tea per day during pregnancy; smaller amounts should be used during breastfeeding. Use raspberry for no more than a week when trying to build your milk supply. Small amounts of raspberry leaf are used in combination with other herbs in recipes. Raspberry leaf is also used in commercial tea products.
Availability: Teas and bulk quantities are generally available in natural food stores.