The online picture database of the Swiss Landesmuseum in Zurich contains 4 pictures of tablecloths from the period 1200-1600.
According to Jenny Schneider, this is the oldest known whitework tablecloth, dating from 1200-1250.
This is a very elegant tablecloth from the first half of the 15th century:
This one is very funny: an early 16th century tablecloth embroidered with food and cutlery:
And one from 1561 embroidered with biblical scenes:
If for some reasons the links don't work, go to the homepage of the online catalogue and insert "tischdecke", German for tablecloth. (the site is in German, French and Italian, but unfortunately not in English):
These books include more detailed pictures and descriptions of these tablecloths:
Schneider, J. (1972), Schweizerische Leinenstickereien, Bern: Verlag Paul Haubt
Trudel, V. (1954), Schweizerische Leinenstickereien des Mittelalters und der Renaissance. Bern: Paul Haubt Verlag