| A boydyke who is attracted to other boydykes - with the attendant logic that the boy parts of them influence the dyke part in such a way that boydyke + boydyke = a very queer gay boy pairing of dykes.
What?? (everyone reaches for their downvote key)
Maybe I should break it down more.
Boy
This is a quirky little word. Besides its standard meaning, it can refer to the partner in the younger role of a daddy/boy relationship. It can be a slang term for someone boyish who wasn't born a boy, like a boyish lesbian or a trannyboy. It used to be a verb, which Webster explains as "to act as a boy," or an "allusion to the former practice of boys acting women's parts on the stage." As Shakespeare had Cleopatra say in Antony and Cleopatra,
....Antony
Shall be brought drunken forth, and I shall see
Some squeaking Cleopatra boy my greatness
I' the posture of a whore."
It's like that song by Blur...
Girls who are boys who like boys to be girls who do boys like they're girls who do girls like they're boys....
Dyke
There's an old lesbian joke:
"What's the difference between a dyke and a lesbian?"
....
"About $30,000 a year."
In other words, "dyke" is often seen as the more radical, unconventional term, trading potential privilege and assimilation for the freedom to express uninhibited queerness. In this situation, it is the core of the term, the background coloring for the word: boydykefags have grown from lesbian and bi women's culture. To put it in faux-grammatical terms, "boy" and "fag" here modify dyke.
Fag
This is another word with many shades of meaning. Gamaliel writes, "In British public schools, a fag is a young student who runs errands and does chores for an older boy." Elsewhere (and increasingly in the United Kingdom itself) it refers to a gay man, but carries the connotation of being flamboyantly gay or flaming. As Homer Simpson says,
I like my beer cold, my
TV loud, and my homosexuals fuh-laaaaming!
Queer pop culture aside, this is the part of the word that indicates that these are in some way boys who like boys. The "fag" suffix (probably the only place "fag" is used as a suffix!) means that these boygirls like each other for their boyness, that those aspects of them relate as gay men.
More than the sum of its parts
The term "boydykefag" combines aspects of all of these words. The people I know who identify as boydykefags are boyish queer women who find themselves to be pretty much exclusively into other boyishly-identified grrlz or genderqueers, and feel like they're expressing a very gay male sexuality together.
I've been seeing an increasing amount of women exploring their "inner gay men," in lesbian and bi erotica as well as in more everyday writings about gender; for example, bisexual author Jill Nagle wrote an essay entitled "Stroking My Inner Fag" in the anthology PoMoSexuals. In calling themselves boydykefags, trans and other queer people are testing the fluidity of gender and sexual identity. | 
