Would K in this case stand for "constant" or "kelvins"

In context;

Nitric oxide and bromine at initial pressures of 98.4 and 41.3 torr, respectively, were allowed to react at 300. K. At equilibrium the total pressure was 110.5 torr. The reaction is as follows.

2 NO(g) + Br2(g) --> (reversible) 2 NOBr(g)

The K is not italicized..

I would think it implies Kelvins because the number is 300, fairly close to STP. I believe that it is technically incorrect to list Kelvins as "°K" or "Degrees Kelvin" due to some scientific nomenclature related reason. At least that's how my engineering professors taught it. I don't think that the question is trying to convey any information regarding equilibrium or anything by the mention of this figure.

So probably Kelvins.

im not familiar with Chemistry but i suppose you emphasis on italics means K is in Kelvin referring to temperature as opposed to a smaller k, referring to a constant. Since you also mention a "reaction" at 300k i would assume the combination of both chemicals is meant to react in some way generating energy translated in heat.
There for temperature in Kelvin falls within the context of heat.

K is for Kelvin but you have to find eq.const.K
Suppose 'x' torr of Br2 have reacted then pressures of each gas
P(NO)= 98.4-2x P(br2) = 41.3-x and P(NOBr) = 2x or
98.4 - 2x + 41.3 -x + 2x = 110.5 whence x=29.2
P(NO)= 98.4-2(29.2) =40 ; P(br2) = 41.3-29.2 = 12.1 and P(NOBr) = 2x 29.2 = 58.4

and K = (58.4)^2 / (40)^2 x 12.1 =0.176 torr^-1

In the context of the question, this is definitely talking Kelvin.

When discussing chemical equilibrium you also use a capital K to signify certain constants, but they also tend to have subscripts that let you identify them.

Kelvin

k is kelvin