I am very new to SEO so I apologize if this question seems basic. If I have a site that relies on outgoing links, however the links are routed through an internal link (e.g. to link to amazon.com/product/idnumber my site routes the user to mysite.com/outgoinglinks/amazon_product_id ) will this negatively affect my SEO as it appears that it is not an outbound link?
Search engines follow redirects so this won't affect SEO unless you are blocking the redirect script (which you shouldn't be doing). The final destination of the link after redirects will get credited for the link.