The bolt handle moves sometimes when I shot my Discovery Rifle! If flops up a little, but does not open, is that normal?

Yes, this is normal.

This something we have heard about in the past.  It happens on some guns and not on others. There is nothing but gravity holding the handle down but as long as the bolt deoe not open, there is no malfunction. 

It is possible for the O-ring on the bolt nose to be missing and if this is the case, a replacement may be purchased from Customer Service.