The 1 foot pipe on bottom of the support plate vibrated off twice when we were putting the siding back.can secure it with self tappers?

The 1' length of JSC Chimney should be twist-locked onto the female coupler underneath the Wall Support Plate. That normally is enough to keep it in place. However if you wish to secure it with a screw, that would be fine. You should have about 1-1/8" of overlap (where the upper end of the pipe & the female coupler overlap) where you could insert a stainless steel screw. The support plate itself should provide protection from rain/weather where the screw has been added. If you plan on only removing the Tee Cap for cleaning purposes though, you could add some silicone to the screw penetration point.