I heard, from a Korean educational radio, “Pay attention ‘camera’ is pronounced with two syllables.” I guess it means that the word was pronounced as not /ˈkӕmərə / but /ˈkӕ-m-rə /. Do you not count as a syllable, in this case /m/, when there’s no vowel sound?
In this example, /m/ is the coda of the syllable /kӕm/.
Syllabic [m̩] rarely occurs outside of the suffix -ism or a few other words (such as chasm or blossom). In this case, we can rule it out because /m/ does not follow a consonant made at the same point of articulation, or indeed a consonant at all; since it can't be syllabic [m̩], we're left with the options of onset or coda; since the vowel following /m/ is elided, it cannot be the onset of /mə/; therefore the only option left is the coda of /kӕm/.
The loss of the unstressed syllable in camera is called syncope.
Snailplane has already explained it quite nicely, but I thought I'd add some information about syllables and syllabic /m/.
Syllabic /m/ can chiefly be found in the suffix -ism as snailplane said in their answer. However, it can also be found in many other words in which it's preceded by an obstruent (/z, t, ð/): as in prism, bottom, rhythm, respectively.
In present day English, it's increasingly common to syncopate (elide) the vowel in the syllable following the stressed syllable. For instance, family used to be pronounced with three syllables; /ˈfæməli/ (it's still common in some British and American accents, however), but the vowel in the syllable following the stressed syllable has been syncopated by many speakers, so you will hear most speaker pronounce it /ˈfæm.li/.
The same goes for camera; it was pronounced /ˈkæmərə/ (with three syllables), but most speakers have reduced it to just /ˈkæmrə/. There are many other examples such as comfortable, chocolate, average etc. [The bold vowel has been syncopated by most—not all—speakers]
Both the pronunciations are perfectly correct.
As for the syllabification of camera, there isn't a widely agreed on answer to that! A caveat to readers: what I'm going to say about syllabification is highly controversial and complex.
There are phonological theories, but are much more complicated than you might think. One of the theories is Maximum Onset Principle.
Camera, when pronounced with two syllables, can be syllabified as /ˈkæm.rə/: we can't syllabify it as */ˈkæ.mrə/ or */ˈkæmr.ə/.
This is controversial. Most phonologists think it isn't allowed to end a syllable with short vowels like /ӕ/, so the above syllabification isn't possible.
There's also another theory that suggests that stressed syllables should not have an empty coda, this would mean that /ˈkӕm.rə/ is preferred.
Yet another theory states that lax vowels such as /æ ɛ ʌ ɪ/ cannot have an empty coda (English doesn't have words that end with those vowels), in which case the /m/ is ambisyllabic; it belongs two both the preceding and the following syllable: /ˈkæm.mə.rə/.
For syllables and syllabification, the following answers may also be helpful