I don't think that having multiple links to your sitemap has any negative consequences at all, any more than having a link from every page to your home page has any negative consequences.
Many site do this. Mine, for example, has a "header" with links to my major pages, including home page, site index, site map, etc., on every page in the site.
This isn't "spamming" in any sense - they are simply internal links designed for visitors to the site, rather than search engines, making it easy for visitors to get back to important pages from any point in the site. The sitemap is included in that group because some people prefer to navigate from there rather than from an index page.
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