So in most accents of English, /r/ is fricated when it follows /t/ and /d/ word-initially, and in some it has become a full affricate /tʃ/. If you were going to look at a spectrogram of this, how could you measure the degree of frication of /r/? I'm looking at the affrication of /tr/ and /dr/ and need to know how it differs from just /r/ being fricated.
The short answer is that there is no difference. Phonetically speaking, an affricate is just a stop closure followed by a period of frication, so [t] plus frication is the same as an affricate. The distinction between an affricate and a stop-fricative sequence is really a phonological one, where the former behaves as a single phoneme and the latter behaves as a sequence of two phonemes. See the related question: Is there a difference between an affricate and a plosive+fricative consonant cluster?
In the case you are talking about, we know there are two phonemes at play--/t/ and /ɹ/. Following the conventions that linguists use for bracketing, this sequence doesn't strictly speaking "become" /tʃ/, since that would indicate one phoneme sequence becoming another phoneme entirely, which only makes sense in a discussion of diachronic change; in a synchronic context, it's more accurate to say that the underlying sequence /tɹ/ is sometimes realized as something like [tʃɹ] (note the square brackets, indicating a phonetic realization). See the related question: Why are /t/ and /d/ sometimes affricated before /ɹ/ in English? Technically, it is the aspiration associated with the initial /t/ that is turning into a fricative, so from a phonological point of view it might make more sense in all cases to think of this process as the affrication of the /t/ rather than the "fricativization" (or spirantization) of the /ɹ/. In practice, however, it might be difficult to say where the /t/ ends and where the /ɹ/ begins in the spectrogram, since the tongue usually gets in position for the /ɹ/ before voicing kicks in, i.e., during the apiration/fricative noise.
As for how to "measure" the degree of frication in the /tɹ/ on a spectrogram, it's not clear how you would quantify such a property, but the main visual difference between frication noise and aspiration noise is that formant structure is visible in the latter but not in the former.