Can you create your own class on operation flashpoint 2 dragon rising

No. At no time, either online or offline can you create a custom class or select your weapons before combat.

However, you can choose from a number of preset classes online which are determined by their role in game. Also - at any time you can loot weapons from fallen soldiers and ammo crates, although much of the time you never see 80% of the guns out there :(

i.e. Support gunner - has support gun.
AT gunner has anti-armour weapon

etc

Note: I don't know weather this applies to PC version, however I have a feeling this would only be possible with a player MOD.