The preferred pronunciation is DOCK-truh-nl (with the accent on dock), not dock-TRY-nl (with the accent on try).
Yes, I know that dock-TRY-nl is the standard British pronunciation, that U.S. academics (especially law-school academics) like to emulate the Brits, and that the British pronunciation is included as an acceptable alternative in many American English dictionaries. But the Brits are notoriously weird (at least to American ears) in their pronunciation habits. Unless you’re willing to adopt their favored pronunciation of urinal as yer-EYE-nl, or of skeletal as skuh-LEE-tl, or of laboratory as la-BOR-a-tree, you should avoid taking their advice on how best to say doctrinal. And unless you want to sound like a pompous academic trying to impress an effete colleague, I recommend that you stick with the standard American pronunciation of words like doctrinal, urinal, skeletal, and laboratory.