How much air ventilation required for oil burner in a closet?
According to NFPA 31, you'll need two openings. One near the top, and one near the bottom. Each of which must be 1 in.² per 1000 Btu/h of the input rating of all the appliances in the confined space.

NFPA 31 Standard for Installation of Oil Burning Equipment.
Chapter 5 Air for Combustion and Ventilation.
5.4 Appliances Located in Confined Spaces.
5.4.1 All Air Taken from Inside the Building.
5.4.1.1 The confined space shall be provided with two permanent openings as shown in figure 5.4.1.1, one near the top of the space and one near the bottom.
5.4.1.2 Each opening shall have a free area of not less than 1 in.² per 1000 Btu/h (140 in.² per gal/h) (22 cm²/kw), based on the total input rating of all appliances in the space.