For syrup, in a stainless-steel, enamel, or nonstick 4-quart Dutch oven, combine 1 cup of the sugar and the water. Cook and stir until sugar dissolves. Bring mixture to boiling. Stir in rose petals. Remove from heat. Using the back of a wooden spoon, slightly mash rose petals. Cover and let stand for 30 minutes. Strain mixture through a fine-mesh sieve set over a large bowl. Discard petals.
Meanwhile, finely chop rhubarb. In the same Dutch oven, combine rhubarb and the strained syrup. Bring to boiling over high heat. Reduce heat to medium; simmer for about 2 minutes or until rhubarb is tender. Measure 4 1/2 cups of the rhubarb mixture; return to the Dutch oven. Stir pectin into rhubarb mixture. Bring to a full rolling boil over high heat, stirring constantly. Stir in the remaining 5 1/2 cups sugar. Return to a full rolling boil, stirring constantly. Boil hard for 1 minute, stirring constantly. Remove from heat. Quickly skim off foam with a metal spoon.
Ladle hot jam into hot, sterilized half-pint canning jars, leaving a 1/4-inch headspace. Wipe jar rims; adjust lids.
Process filled jars in a boiling-water canner for 10 minutes (start timing when water returns to boiling). Remove jars from canner; cool on wire racks.