JAKARTA, Indonesia— An online magazine catering to supporters of the Islamic State in Southeast Asia is not the first place you might expect to find a spread featuring an illustration of a pink flower. But there it was amid articles about beheadings and bombings in an issue last year of Al-Fatihin, or The Conquerors.

At first glance, the image could be mistaken for a misplaced advertisement. But the title above it left no doubt about the article’s intended audience: Jihad Wanita, or “Women’s Jihad.” The following six paragraphs outlined the different forms of jihad a woman can carry out, such as caring for wounded soldiers or supporting jihadis in battle. In another issue of Al-Fatihin, a black-and-white photograph of a woman standing alone, firing a rifle from behind a barricade, accompanied an article that trumpeted the courageousness of Muslim women in the Islamic State and urged them to take up armed struggle against unbelievers…