Yes, if your partner does not mind, go for it. Put an old towel under you and enjoy it.
Some women are very horny during their periods. Some men are the same. When I am on, it is like waving a red cloth in front of an angry bull with my husband. He says he does not know how he do it but he knows when a woman if flowing. It must be a smell or pheromone that his nose picks up without him realizing.
Be careful and make sure every thing going into you is squeaky clean. Your cervix is more open during this time so you can get an infection easier. If you are not sure about your partner's sexual health, he should wear a condom.
The contractions in your uterus can change your flow a bit. It can force more flow out quicker and make your period shorter. Some women also say that it helps for cramps and PMS symptoms.