These are three of your events (I've put them close together, but they are still in the order they are in the event sheet)
if up and right are both down, all of these conditions are true and so all actions will be executed.
Construct reads from top to bottom
so first it sets animation up up from the beginning
then it sets animation forward from beginning
then it sets up up from the beginning
it does this every tick, and because different animations are called
the animation will every tick be restarted from the first frame and as such seem not to run at all
The trick is to add conditions, so only one of these events is true when both keys are down.
adding inverted statements does the trick most of the time, although it's not the prettiest method
In this case you only have to add an up-key is not down condition (right-click invert "up key is down"-condition)to your right key is down event, for both other events have the same action attached.