There are definitely some images that would be popular in both medieval Islamicate societies and Christian societies, although I don't know that they would be embroidered on handkerchiefs. One possibility would be griffins and other real and fantastic beasts which are often found in medieval Islamic textiles(see for example this Spanish fragment http://www.metmuseum.org/collections/search-the-collections/451473 o) but which were appreciated by Europeans and are often depicted in medieval painting(see for example this Madonna, which contains what appears to be a rug with fantastic beasts that to my mind looks Spanish or Silician: http://www.nga.gov/content/ngaweb/Collection/art-object-page.3.html). One could also depict beasts with especially strong noble associations such as lions; probably the most famous example of that is the coronation cloak of Roger II of Sicily(http://en.wikipedia.org/wiki/File:Weltliche_Schatzkammer_Wienc.jpg), embroidered with an Arabic inscription by probably Muslim artists for a Christian king. If you would rather do something more figural, courtly life is always an option. Hunting and falconry in particular were emblematic rituals of royalty and nobility in both medieval Islamic and European art and in the Islamic world at least go back to a very, very ancient Near Eastern iconographic motif of the king as hunter. As such, these scenes would be an eminently appropriate as decoration for an Umayyad emir's robe, a saint's reliquary casket, or a Genoese merchant's treasures. This is one such example of a hunt scene in a medieval textile from early Islamic Syria(http://www.metmuseum.org/toah/works-of-art/51.57), and here is a Coptic textile with similar hunt motifs(http://images.rom.on.ca/public/index.php?function=image&action=detail&sid=&ccid=]). These images would have resonated at this point as vestiges of a more general late antique iconography of royalty and cultivated leisure. Although most of what I am looking at here is Islamic(mostly because there are several regions of the Islamic world that are especially well-known for preserving textiles and because many Islamic textiles survived by being reused in European liturgical contexts), they were appreciated in other contexts as well.

One last non-handkerchief option that might actually be interesting if he's interested in medieval Islamic history and you know Arabic or can get someone who knows Arabic to do the inscription for you is a kind of textile called a tiraz. A tiraz is a decorated arm band on a garment with an inscription, usually beginning with a standard blessing formula("In the name of god, the compassionate, the merciful...", the name of the ruler who gave out the garment, and the recipient. This sort of gift-giving was actually a very important part of many court cultures, with rulers establishing their power and supporting their subordinates or vassals by giving clothes to them. Thus for example when Gagik Artsruni was made prince of Vaspurakan in western Armenia he received a robe from the representative of the Abbasid caliph as a token of recognition from the caliph. This painting of the Armenian King Gagik of Kars gives a sense of what such dress might have looked like: http://armenianstudies.csufresno.edu/iaa_miniatures/image.aspx?index=0176 and in fact you can see the tiraz in this(they're the white armbands). This is a fine example of a surviving tiraz, made in Nishapur in modern-day Iran: http://www.metmuseum.org/Collections/search-the-collections/448603?rpp=20&pg=1&ao=on&ft=tiraz&pos=4#fullscreen

Was there a particular problem with the answer to the question three days ago?