Based on your 90G tank i'd say 3 would be the most. Two would work if a pair formed. I had a pair of barletts in my 125G for 9 months and never had an issue.
I'd be prepared to feed 2-3 times a day of meaty frozen foods. I would consider a top a must with all tanks
Bartletts are on the aggressive side for anthias, though they are very hardy. A group of 5 ignitus is an excellent choice for a 90g. Ignitus are more peaceful than bartletts and stay in a group far better as well. Some anthias that do well singly include sunburst, borbonius, pink square and bimaculatus. Other species that would do well in a group in your sized tank are dispars, randalls and pulcherrimus.
I've had better success with a pair of bartletts as opposed to a small harem, same with my lyretails.
This makes sense because bartletts and lyretails are more aggressive than most anthias.
Ignitus should be fine in a group of 3 or 4, but I personally recommend 5.
I havent had much success with the purple queens or flavo's. I wonder if it's because those are more deep water?