I don't know of any community where "rəˈɡälyə" (IPA /rəˈgɑːljə/) has become an established pronunciation (it's not listed in any of the OneLook-indexed dictionaries), so I would avoid using it, and recommend pronouncing regalia to rhyme with "Australia" instead.
Some Latinate words spelled with the letter "a" show variation between "long" /eɪ/, "short" /æ/, and a "restored" quality /ɑː/, but this is highly dependent on the identity of the specific word. For example, /ɑː/ has become standard for whatever reason in the word drama, but seems to be pretty uncommon in data (see Alex B.'s answer to "Data pronunciation: “dayta” or “dahta”?"). There are sometimes differences between dialects: e.g. /eɪ/ in dahlia is more common in British English than in American English, according to Merriam-Webster.
I found a Reddit conversation that confirms that you are not the only person who has thought of using /ɑː/ in "regalia":
I'm guessing you say regahlia instead of regaylia just based on your taste. Is that true?
–asphyxiate, Wed Aug 16 23:20:56 2017 UTC
I do say regahlia, you're right! I was sad when I realised that azure wasn't pronounced azooooerr; some words just taste better mispronounced.
–sushideception, Wed Aug 16 23:56:34 2017 UTC
("I have synesthesia, which allows me to taste words. AMA!", casualiama Reddit)