I just went thru the same experience as many others. I booked a flight and received a request confirmation. After that nothing. I managed to find an email address for them (service...), but no phone no. And I was in a panic - because it is high season and I was looking for a continuation flight from BKK to Koh Samui. Any delay and no seats!
A day later I got a reply saying there was a problem with my address. I replied that it was indeed my adress, but after that nothing. I found a number on sitejabber tho and called. I'm in Cyprus (GMT-2 hrs) and I got a message about flights24 taking calls between 9 and 6 PST (ie, sometime during the night here). More panic. I sent them multiple emails marked urgent and containing several phone nos. At which they could reach me. Nothing. Finally I sent a nasty to them, said that they should not process any reservations for me and not to take my money - which included several high fees (like $68 for using a credit card - how else can you book on the Internet?).
I will certainly consult sitejabber before proceeding again with a site that I don't know!