tl:dr - Lesbian here, and I don't really like Pride month very much these days.
There's no straight pride or flags but that's okay, straight people have basically all the representation in day to day life. All the disney princesses have their disney prince (mostly), almost all romances in books, TV shows, films, everywhere, are straight. Straight people don't have to come out because it's the default expectation.
People say children shouldn't be exposed to the fact that gay/lesbian people exist - but straight romances, relationships and what these should look like are in children's stories and TV shows from birth. It's acceptable for Belle to fall in love with a not human beast who is essentially keeping her prisoner, but people lose their mind that Peppa Pig's mate has two mums.
No hate for Beauty and the Beast, it's just illustrative of the way society projects relationships.
People equate gay/lesbian representation to sex education but this is not the same. Just like it isn't for straight people and obviously, like everyone else, believe that sex education should be age-appropriate.
People (not saying you, but some people) will say to my DS who is friends with a girl - oh I wonder if they will end up together. They're 3!
Most people don't care about other people's sexuality these days, not as a grown up anyway, but it's hard as a child/teen growing up with very little representation in the mainstream media. And then having to tell people about it eventually.
Gay/lesbian people are more likely to have addiction/mental health/self harming issues generally because society is not kind to us growing up.
So no, there's no straight pride, but it's not the same experience growing up and gay/lesbian people have more to contend with in our formative years - from a sex/relationships perspective, obviously individuals have their own challenges and traumas growing up!
Sorry for the rant, and whilst I understand and agree pride month is just rainbow-washing, straight people who complain about not having their own pride is like men complaining about not having international mens day. Everyday is mens day! That's why women would rather be stuck in the woods with a bear than a real life man.
Having said all that, pride month has turned into a rainbow-washing meaningless show of inclusion, but no actual action to make their organisations more inclusive. If an organisation really cares about inclusion there's plenty of action they can take that doesn't involve a single rainbow that can make a big difference.