Is there a specific reading for 常訓 and 常音? I see this in an electronic dictionary to indicate on'yomi and kun'yomi reading of kanjis. What I struggle to find is the meaning of the combination of both kanjis (常 + 音 or 訓), is it meant to be read as a single word (常訓 and 常音) or as separate kanjis? like 常訓 meaning maybe つね くん, regular kun'yomi?
As noted by naruto in the comments, neither of these are regular words, and both look like abbreviations. I suspect that 常訓 is short for 常用【じょうよう】訓【くん】読【よ】み, and that 常音 is short for 常用【じょうよう】音【おん】読【よ】み. Consequently, if sounded out, 常訓 would be じょうくん, and 常音 would be じょうおん.
Dictionaries are horrible when it comes to abbreviations. Historically, this was due to the high cost of printing and publishing. Nowadays, with electronic media, it's a kind of pernicious inertia: there's no space restriction anymore, and there's no cost restriction anymore, so it would make vastly more sense from a usability and understandability perspective to spell things out. But old habits die hard.