There are now several major airlines flying to Colombo, with a choice of direct flights or stop offs
After arriving at Bandaranaike International airport you have a choice of air, rail or road to get to Trincomalee. Internal flights are available to Trincomalee, Cinnamon Air and Helitours are the most popular providers. Buses leave every few hours from Colombo main station, there is an AC luxury bus that leaves each evening.
There is one overnight train, schedules can be checked here: