Evie....tomh is partly right. Kilz is marginal at best - there are better stain sealers - B-I-N being one.
For you application however - tomh is correct - DO NOT USE KILZ - not to save money though.
Kilz is designed only for spot priming outside (even though this is the inside of the shed - I assume it isn't heated?) It dries so hard that it doesn't have the flexibility to move with the temperature changes that exterior surfaces face. If you use it on large surfaces outside - it will come off - and your paint with it!
Kilz can be used on large areas inside - but is really only a stain sealer - it doesn't hide very well. For example - if you had a smoke stain - you might use Kilz - to SEAL the stain from bleeding through the topcoat. If however you were trying to hide a dark color when going over with a lighter one - a product that HIDES well - like Glidden Ultra-Hide Gripper - would be better suited.
Anyway......as tomh said - a good exterior wood primer and exterior finish coat would be the way to go.....