From https://en.wikipedia.org/wiki/Rendaku
Rendaku (連濁?, lit. "sequential voicing") is a phenomenon in Japanese morphophonology that governs the voicing of the initial consonant of the non-initial portion of a compound or prefixed word. In modern Japanese, rendaku is common but at times unpredictable, with certain words unaffected by it.
Rendaku is the changing of voicing that, in practice, is usually the addition of a dakuten/tenten to the first syllable of a word contained within a compound or phrase.
As mentioned above; rendaku occurs commonly but is unpredictable, in that there isn't any fit-all rule that determines when it applies.
However, rendaku commonly appears in words involving the noma iteration mark (々) indicating repetition of the prior character, such as in hitobito [人人/人々、ひとびと, not hitohito] and samazama [様様/様々、さまざま, not samasama]
In your example, きらきらぼし is considered a single phrase in that きらきら is a modifier describing ほし.