If I put more that one video in the landing page then will it effect any affiliate products conversions negatively?
Well you haven't provided much information here. So, we can't help you much in this case.
But I will say that as long as the additional video is relevant and can attract users to buy your product. I don't think that it will be a problem.
I think one video is enough. You don't want to give a bad focus on your visitors.
Once I put three videos in one landing page. It didn't get any sales even through paid advertising.
One video is enough! It will affect the speed of your landing page and it's one of the important in SEO.