Is there a succinct rule for teaching my 3rd grader the usage of gh and ph? I know how to spell words with those diphthongs, but it's intuitive now, rather than by remembering a phonics or spelling rule specifically.
If the concern is using these two consonant digraphs to spell the sound [f], things are pretty straighforward:
The digraph 'gh' spells the sound [f] only after short vowels spelled with a vowel digraph, the second letter of which is 'u': cough, enough, laughter, rough, tough, trough. It never spells [f] in either word-initial or element-initial position. And it only occurs in native English words.
The spelling 'ph', however, spells [f] in words borrowed from Greek and a few from Hebrew. Most often, the digraph 'ph' spells the sound [f] in word-initial position: pharmacy, phase, pheasant, phlegm, phobia, phone, photo, phrase, physical. It often clusters with 's': asphalt, asphyxiate, sphere, sphinx. In the middle of words it is often in element initial position: aphasia [a+phas+ia], cellophane cell+o+phane, diphthong [di+phthong, emphatic [em+phat+ic], microphone micr+o+phone, prophecy [pro+phec+y]. And finally, 'ph' often spells [f] in the middle of elements: alphabet, catastrophe, decipher, gopher, nephew, orphan, pamphlet, typhoon, or at the end: telegraph, triumph, trophy, typhoid. In short, the 'ph' spelling can pop up most anywhere in a word, but never after a short vowel spelled with a vowel digraph ending in the letter 'u'. (In a few not-so-common words 'ph' spells [f] after a digraph ending in 'u', but in each case, the vowel spelled by the digraph is long: dauphin and words with the prefix eu- meaning "good": euphemism, euphony, euphoria,, etc.)
So summing up, the digraph 'gh' only spells [f] after a short vowel spelled with a digraph ending in the letter 'u' and never at the front of a word or element. But 'ph' spells [f] in all positions, though usually at the front, and never after a short vowel spelled with a digraph ending in 'u'.
An aside: Technically 'gh' and 'ph' are not diphthongs; they are consonant digraphs. Diphthongs are two vowel sounds that combine into one (as the Greek source of diphthong suggests: [di+phthong "two sounds"). Consonant digraphs are two consonant letters working together to spell a single sound: 'sh', 'th', 'gh', 'ph'. Most often in American-English, diphthongs are spelled with vowel digraphs, as in grouch, house or boil, hoist. But in some dialects long 'a' and long 'i', as in tale and tile, are pronounced as diphthongs even though they're not spelled with vowel digraphs.