does a Kanji's Onyomi always have the same pitch accent?

for instance 正(しょう）　in 保険証（ほけんしょう） is high low. Does that mean it will always be high low in any compound(or most of them)?

Nouns' pitch doesn't usually change, except in compounds. Although the head of the second word of compounds tends to get the core accent, it's not always the case.

"The pitch accent of a kanji" doesn't make much sense. It's words that have pitch accent. For example, 殺意 (さつい) and 殺人 (さつじん) both have 殺 (さつ). But, in standard Japanese, さ is accented in the former while this is not the case in the latter compound. So just because you have a native Japanese speaker pronounce the on-readings of kanji A and B out of context doesn't mean you can get the pitch pattern of compound AB.

As for 証 (This is not the same kanji as 正, by the way.), I pronounce 保険証 without a pitch drop when I fake standard Japanese (i.e., if you write it with H (high) and L (low), it'd be like LHHHH). Here are a couple more examples: 証拠 (しょうこ) would be LHH if said alone out of context. But it becomes HLL with the second L (i.e., こ) lower than the preceding L if it follows 状況 and forms the word 状況証拠.