2mm clearance between the chainstay and the rear tire I use a pair of club roost cross terra (27 1 3/8) on a vintage raleigh bike (maybe it's raleigh record). Originally the bike had 27 1 1/4 tires.
If I'm correct, 1 1/4 is 32mm wide and 1 3/8 is 35 mm wide.
The clearance between the chainstays and the rear tire is 2mm on both sides. Is this acceptable? 
The brakes are just fine and I only use the bike for daily commuting.
Clearance is clearance.  It will work fine until your wheel goes out of true, or you ride in conditions that produce 2mm of extra width on your tire (mud, snow, etc).  Or alternately some combination of the two.  Depending on your frame material (I am too lazy to look yours up, but I'll assume steel) it will probably rub on almost every ride at some point when you flex the frame enough for it to touch.