How should the nonsense word 'frabjous' be broken down into its constituent phonemes (e.g. the consonant blend -fr)? I would like to determine how this word is regular in English phonotactics.
You don't "break down" words into phonemes, you first transcribe a spoken word into a language-neutral alphabet which represents how the word is actually pronounced, and then you analyze the transcriptions according to some principles of phonemic analysis to decide what phonemes are present. The first task is extremely difficult (requires extensive training). In fact, very few linguists actually real in the process of converting speech to phonetic transcriptions. When you look up a (real) word in a dictionary, they often will give you a phonemic analysis of the word in question. In fact, you can just look up the phonemic transcription of "frabjous", which Wiktionary claims is [ˈfɹæbdʒəs]. Webster's agrees, though they use a different transcription system.
Terms like "vowel blend" and "consonant blend" don't mean anything in linguistics, and while I have heard the trms I can't remember what they are supposed to mean. Probably you should find an English teacher's forum, where is where it is probably used.
Typically, when a person transcribes a word, they speak the language and have already learned the phonemic analysis of the language (someone else has worked out the details), and they are implicitly applying that analysis to some word, maybe trying to decide what the first vowel of "economic" is (it varies according to individual). The approach is very different if you are starting from scratch, aiming to devise a scientifically-accurate analysis of a language working with a speaker, where you do not start with already-made decisions about how the language works.
As for conformity to rules governing phoneme sequences, that depends on what you think those rules are. A very common view is that phoneme sequence is subject to rules regarding syllables, i.e. in English [pr] is possible in a syllable onset but not in a syllable coda; [nt] is possible in a syllable coda but not an onset; [sp] is allowed in both the onset and coda; [pw] is not allowed in any syllable constituent (but it may result from concatenation of a coda plus an onset). A generally-accepted view of syllable-sequencing rules is that they contain at most two elements, thus a rule can "allow" [sp] or [pr] but no rule "allows" [spr], instead that has to come from two overlapping rules.
Such a simple theory of phoneme-sequence restrictions might be right, were it not for the fact that there are simple *ab restrictions that aren't just about building branching onsets of codas, such as the lack of voiceless stops after a nasal in a number of languages. This underscores the well-known fact in phonological theory that the set of "possible sequences" not only involves "possible syllabifications", it also involves applying all of the rules of segment-change in the language (where often /nt/ → [nd]). That then means that you also have to know what the rules of English are, so that you can see whether some rule failed to apply in a candidate word.
People often apply analogical reasoning and intuition to these question, so even though [blɪnt] is not a word of English, people reason from analogous words like "blink, blimp, plinth, Clint, blunt" to conclude that such a word is "possible". This is not just about language, in general people look for similar cases to decide is something is "possible" – they may be wrong, because "possible" is really a question about underlying causal mechanisms and not "similarity". We simply hope that our similarity judgments have a relation to causal mechanisms.