There are no direct scheduled flights from Birmingham to any Croation airport, so it's not possible to find this answer from a web search. (I assume that you've booked a hoilday on a charter flight). Additionally, you've not stated which airport in Croatia you'll be flying to. Therefore any answer will have to be a bit of a 'guesstimate'. Based on Croatia Airline's service from London to Split, which is scheduled to take 2 hours 20 minutes, I'd guess that a flight from Birmingham to most Croatian airports would take around 2hrs 45 mins.
Chris