Demiboy (also called a demiguy, a demiman, or a demidude person) is a gender identity describing someone who partially identifies as a man or boy. In addition to feeling partially like a boy or man, demiboys also feel partly outside the binary. That can include anything under the non-binary umbrella like agender, genderqueer, or xenogenders for example.
The first known recorded instance of someone referring to themself as a demiboy was August 12th, 2010 by a user named Bad Patient on AVEN,
“...I said to myself that I can any word relate to me if I just stick a "demi-" in front of it. And then I realized that it might actually help me find a word for my gender identity. I've felt for some time that I may have too much of the masculine element in me to call myself agender and feel good about it — so maybe it would be a nice idea to call myself a demiguy. Demidude. Demibloke...” 
However Bad Patient goes on to say they weren't being serious.
In response, the user Am I Human claimed that the people who worked on the wikis for demigenders had been coined there. But no exact dates can be found, and the definition is slightly different to the most common definition used today. The given definition is "...either someone AMAB who feels the barest association with manhood or an non-binary AFAB person who is transmasculine, and feels a vague association with masculinity".
"Demigirl" and "Demiguy" were added to the AVEN Gender Definitions Masterlist on December 12th, 2010.
The blog owner, Marilyn Roxie, had collected data for a survey of genderqueer people that year, (September 15th - October 15th) and added demiboy and demigirl as options. Nine people selected "demiboy", and seven people selected "demigirl".
This lead to an increase in awareness and by early 2014 the prefix demi- was commonly known in relation to genders. At an some point between October 2011 and 2014 the common definition of demiboy shifted from the previously stated definition to "someone who is partially a boy".
On August 24th 2015, an unknown Tumblr user made an alternative flag. Also in August, transrants made their own alternative flag. Sometime that same year, Rockabilly Punk made an alternative flag too.
July 9th 2016, an unknown DeviantArtist made an alternative flag for demiboy.
Flags + Details
The demiboy flag holds meaning within its colors. The white represents non-binary part of the gender, light blue represents the partly boy aspect, and both grays represent the spectrum within the other part of being a demiboy.