Heterosexual, usually shortened to straight, describes emotional, romantic or sexual attraction primarily to people of a different gender. Heteroflexible describes being mostly straight with occasional same-gender attraction. Homoflexible describes the mirror.
Definition
Heterosexual describes attraction primarily directed at a different gender from one's own. It is the most common orientation and, in most European societies, the assumed default, which is what the word heteronormativity points at.
The word "primarily" is doing real work there. Most definitions of heterosexual, including the ones used in survey research, allow for it to be a predominant pattern rather than an absolute. That is exactly the space heteroflexible occupies.
What do heteroflexible and homoflexible mean?
Heteroflexible describes someone whose attraction is predominantly to a different gender, with occasional attraction to the same gender. Homoflexible describes someone whose attraction is predominantly to the same gender, with occasional attraction to a different one.
Both name a lean with exceptions. On the Kinsey scale they sit roughly at 1 and 5: not exclusively one thing, not evenly balanced either. Both are usually chosen by people who want to acknowledge the exceptions without adopting bisexual as their primary word, often because "mostly straight" or "mostly gay" is the honest headline and bisexual would overstate the balance.
This is contested vocabulary, and the argument is worth knowing rather than settling. Some bisexual people point out that bisexuality has never required equal attraction, that Robyn Ochs's widely used definition explicitly says "not necessarily to the same degree", and that the flexible terms therefore mostly exist to keep a comfortable distance from the word bisexual. Others say the flexible terms describe their experience more precisely, and that being told which word they should be using is exactly what the bi community objects to when it happens to them.
Our position is the same as everywhere else on this site: use what describes you. If you find later that bisexual fits better, nothing is lost by switching. If you find heteroflexible keeps being accurate for twenty years, it was accurate.
Flag
Heterosexuality has no pride flag, for the same reason cisgender has none: pride flags exist to make marginalised groups visible to each other. Heteroflexible and homoflexible have community flag designs in circulation, generally adapting the bisexual palette, without a single standard or a documented designer.
Etymology
From the Greek heteros, other, and the Latin sexus. It was coined by Karl-Maria Kertbeny (1824 to 1882) in a private letter in 1868 and appeared in print in an anonymous German pamphlet in 1869.
History
There is a historical irony worth keeping. Kertbeny was campaigning against Prussian sodomy laws. To argue that same-sex attraction deserved legal protection, he first had to name the thing it was being measured against. Heterosexual was invented by a gay rights advocate as a contrast term, not by a moralist as a standard.
Which points at something larger: "a heterosexual person" as a distinct type of human being is a late nineteenth-century idea. Jonathan Ned Katz's The Invention of Heterosexuality (1995) argued that the entire hetero/homo division is a modern cultural construction rather than a timeless fact about people, and that argument is now standard in the history of sexuality.
Common myths
Myth: heterosexuality is the natural or default orientation
It is the most common one. Most common is not the same as natural, and the others are equally natural variations. The word "default" describes a social assumption, not a biological fact.
Myth: heteroflexible is just bisexual with extra steps
Sometimes it functions that way, and some people do move from one to the other. But a term that describes a strong lean is not obviously the same as a term that does not specify one, and the people using it are the ones who know which is accurate for them.
Myth: straight people cannot be part of LGBTQIA+ spaces
Straight cisgender people are not part of the community as members, and the A does not stand for ally. Straight people with trans partners, straight trans people, and straight parents of queer children all have real stakes, and plenty of them do a great deal of the work.