What I don't get is why, if you don't even pronounce it, you'd add it into the phonetic spelling
The R modifies the previous vowel sound by making it longer. You don't pronounce the "ruh" sound at the end, but the vowel sound itself changes when an R is there. Just like adding an E to the word man makes it mane - you don't pronounce the E but it changes the preceding vowel sound. No becomes nor. Co becomes cor. Adding an R to Da makes it a decidedly long-sounding vowel, whereas Da is a bit more ambiguous (could be long like darling, could be short like dad).
Is there any other way to pronounce Dah other than Dah?
Yes, it could rhyme with hah, which has a short vowel sound in my accent.
Basically, adding an H is a little confusing if you're a non-rhotic speaker, as there could be multiple pronunciations (Ha and Hah could both be long or short, Har is definitely long). Ironically, Adding an R makes the pronunciation less ambiguous (if you're someone with a non-rhotic accent
)
As for Dahlia, I'd pronounce it Daylia. Because that's how it's said here because the English language is a pain in the arse.