It looks to me like you need a front derailleur adjustment. Maybe you just need to refine your shifting technique. If you think that you may be up to doing it yourself, goto the Park tool website and follow their instructions.
What you have isn't chainsuck. Chainsuck is mostly a mountain bike thing that haappens when the chain catches a burr on the front chainring and tries to ride up the backside of the chainring until it gets caught against the frame.