Smith has set up the campaign with entrepreneur Dermot McNamara, after the pair found that homeless women are suffering from health and hygiene problems, as well as social isolation, as a result of being unable to access free sanitary care.
Supplies at homelessness shelters are extremely limited, which is leading to an increase in criminal activity including mugging and shoplifting.
Smith said: "Nothing is luxurious about having a period, and this can't be more true for homeless women. To think that condoms are available from several outlets for free, and sanitary ware is only accessible for those who can afford it, is atrocious and slightly perverse. Women cannot help having periods, it is not a choice we have."
The campaign has already attracted the attention of The Big Issue and Women's Refuge, which have come on board. Celebrities including athlete Rachel Christie and Gogglebox's George Gilby have also pledged their support.
FlowAid is asking the public to place donation boxes for unwanted sanitary products in their offices, donate directly, organise fundraisers and petition MPs.