If you need animations for the flow item while being picked up by an operator, you should follow up on @tanner.p's suggestion and build it specifically for that case.
In principle all the code for the forklift is accessible in FlexSim so if you want you can view and copy it. But the way the forklift animates the item is different from the way operators work so that's not going to be of any use to you!
The forklift consists of different components that you can view when you right click it and select Edit -> Animations. As part of its loading / unloading task the fork component is animated and the item just sort of follows along automatically. In contrast the operator animations are much more complicated: the operator doesn't consist of loose 'components' but it is animated using a bone/joint model which is imported into FlexSim from software specifically used to create that bone animation.