Can my S-Corp LLC business buy office furniture from myself and claim it as a business expense?

Your S-Corp can purchase office furniture from you.  The purchase amount must be the basis you have in the office furniture or its fair market value, whichever is less.  You need to be able to substantiate the fair market value you indicate for the furniture.

IRS Publication  561 provides information on how to determine fair market value for donated property.  The same principles apply to determine value for your purpose.  Here is the link for the publication:   https://www.irs.gov/publications/p561

For example, if you had already fully depreciated the furniture which was used for a prior business, then you would record the asset on your books with zero basis.  If you had purchased the furniture for $3,000 and used section 179 to fully depreciate it, then you still have a zero basis. 

Also, another option would be instead of the S-Corp purchasing the office furniture from you, you contribute the asset in exchange for shares or percentage of ownership.  The same rules would apply in determining what the contribution amount would be -  the basis or FMV, whichever is less.