The reason you can't hear a pronunciation difference is because there isn't one. 

'Our' and 'hour' are pronounced exactly the same.

Hey bro I am a native english speaker and I don't see a difference either

In Collins, the phonemic transcriptions of both words are the same.

When these words are articulated very clearly, then they sound the same and have two syllables, to rhyme with "flower".

When the word "our" is spoken quickly by most people in England, it changes to "aah" or "aar" (rhymes with "far").

Some people might make the word "hour" one syllable, when speaking quickly.  This can depend on accent. In my accent (typical London), it sounds like something between words which rhyme with "flower" and "far".  It's hard to express it in writing!

A comparable change of pronunciation happens in American accents too but I am not able to describe it accurately.

Well, according to Dictionary.com, there is a difference in pronunciation, but only if we say "our" in an informal, casual, unstressed, and I would add lazy manner.

hour = ouuh r, ou-er

our = ouuh r, ou-er; unstressed ahr

But normally I would say the two pronuncaitions are the same.