How do you pronounce "exclamation"?

In American English: /ˌɛkskləˈmeɪʃən/ (ehkskl-uh-MAYSH-uhn). In British English: /ˌɛkskləmˈeɪʃən/ (ehkskl-uhm-AYSH-uhn). In Canadian English: /ˌɛkskləˈmeɪʃən/ (ehkskl-uh-MAYSH-uhn). In Australian English: /ɛksklɐmˈeɪʃən/ (ehkskl-ⱯM-aysh).

Is "exclamation" pronounced differently in American and British English?

Yes. In American English it's pronounced /ˌɛkskləˈmeɪʃən/ (ehkskl-uh-MAYSH-uhn), while in British English it's /ˌɛkskləmˈeɪʃən/ (ehkskl-uhm-AYSH-uhn).