PREPARE boiling water canner. Wash and heat jars and lids in simmering water until ready for use. Do not boil. Set bands aside.
COMBINE kiwifruit, strawberries, pineapple juice and lime juice in a large saucepan. Gradually stir in pectin. Bring to a boil over high heat, stirring frequently. Add sugar and return to a full rolling boil that can not be stirred down, stirring constantly. Boil hard for 1 minute, stirring constantly. Immediately stir in rum and green food coloring, if using. Remove from heat. Skim off foam if necessary.
Carefully ladle hot jam into hot jars leaving 1/4 inch headspace. Wipe rim. Center lid on jar. Center lid on jar. Apply band until fit is fingertip tight.
Process in a boiling water canner for 10 minutes, adjusting for altitude. Remove jars and cool. Check lids for seal after 24 hours. Lid should not flex up and down when center is pressed. Lable and wrap a ribbon if giving for gifts.