Notes for those who can't read IPA:

[k] is an unaspirated k like the "k" in "skill". (not "kill")
[ɯᵝ] is a compressed u like the "oo" in "boot".
[ma] is like the "ma" in "Mark".

The acute accent on ɯ́ and grave accent on a indicates that the first mora/'syllable has a rising pitch, while the second 'syllable' has a falling one.

(side note: The ꜜ on the phonemic transcription /in slashes/ indicates a downstep, or a drop in pitch in the following 'syllable'. It is not used in phonetic transcriptions [in square brackets])

Taken together, you can approximate the sound with Koomah, or Koo↗ mah↘ The pitch rises on "Koo", and falls on "mah". You can approximate the sound with "KOO-mah" (stressing the first syllable, but bear in mind that the the Japanese don't change the lengths of their syllables even when they are 'stressing' their words.)

Also, in Standard Japanese (AKA NHK Japanese, or a specific variant of the Tokyo 'dialect') the "kuma" for bear is pronounced as /kumaꜜ/, with the rising pitch on the second 'syllable', which is subtly different than the "Kuma" for the river that our light cruiser is named after.

(Contrast how Kuma pronounces her name in the game, versus how they call bears in Yurikuma Arashi. Kureha's pronunciation is probably the most distinctive example of the latter.)

Of course, other regions in Japan may pronounce "kuma" (for bear) differently. The Kansai region pronounces it as /kuꜜma/, with the rising pitch on the first 'syllable', like Kuma's name. Tokyo speakers may also use this pronunciation to emphasize the word, especially in a comedic context (possibly as an allusion to the Kansai dialect).

TL;DR: KOO-mah.

English lesson along with some Japanese dialect fact in Danbooru.

Thanks for the translation and the lesson!