I was wondering if Paperback Swap allows posting/trading of magazines?

No, magazines are not allowed here for swapping.  I've seen people use them as incentives for ordering from their shelf though - like posting in Book Bazaar.  But just know that a package with a magazine can't be mailed via media mail.

• Anything that is not a book
• Anything that contains advertising
• Advance Reader Copies (also known as ARC s, Review Copies or Uncorrected Proofs--these are not the final versions of books)
• CD-ROM books/e-books (books that must be read on a computer)
• Burned copies of audio books
• Xerox or otherwise unoriginal copies of books
• Unbound pages
• Leaflets or pamphlets or booklets* without ISBNs (other members complain at spending a credit for these)
• Books that require supplementary non-media materials (non-media materials cannot be sent by MediaMail)
• Pornography (sex manuals and erotica are allowed, hardcore pornography is not allowed)

Magazines contain advertising and cannot be sent Media Mail.