of - ɔf or əf

[keannu]

I was shocked to see this symbol[ɔf] for of and hear the produnciation. Do the British really pronounce "of " as ɔf? I have always heard "əf" and when I heard Korean students pronounce [ɔf], I corrected them.

'of'
of-American [ɑf,əf], British [ɔf,əf]

[5jj]

Unless the word is stressed, 'of' is pronounced /əv/ in the phonemic symbols used in most BrE dictionaries. When stressed, it is pronounced /ɒv/

[keannu]

By /ɒv/, do you mean /ov/ in AmE?
I mean the sound when you should round your lips into a small tight circle. The /ɒ/ is only used in the British pronunciation systems, I guess. The reason why I haven't heard /ɒv/ for "of" is, I guess, they rarely pronounce so even if they do.

[raindoctor]

The first variant is possible, since it falls under the CLOTH lexical set. In some accents, both CLOTH and LOT are merged. Same with with BATH and TRAP lexical sets.