The exact same (in fact more detailed) question came up on the WotC boards. Here is the answer to your question:
Hitting with Thundering Armor while having the Feat Mark of Storm result in a Push 1 and a Slide 1 because Mark of Storm doesn't increase any Forced Movement, it produces one on its own.
Where someone else explains how this sort of rule is adjudicated in D&D 4E:
There isn't a rule which states you can't have more then one forced movement type. So the specific rule present in MoS that you get a slide has nothing to contradict it. 4e is Specific vs General, but it is also Rules Text vs Nothing At All.
So yes, they 'stack'.
Interestingly the OP on the WotC post also adds in the use of the Quickbeam Staff:
Increases forced movement by 1.
This is a property of the
Forceful: Whenever you pull, push, or slide a target with an attack power using a forceful implement, the distance of the forced movement increases by 1 square.
Wondering if it applies to each...
The answer is quite niggly, in that it relies on the emphasized text in the quote above, namely:
Mark of Storm's Slide isn't increased by the Forceful Property because you are not Pushing with an Attack Power, but with a Feat after you Hit wth an Attack Power.
This results in a
(1+1)+1=3 forced movement.