How much data should I have to accurately calculate RSI ?

That's a valid question. Because, in theory, the RSI value for any day takes into account all the previous values before it, therefore incorporating in it even the effect of the earliest available value. This happens in a EMA based system. Ofcourse the effects of previous data points keeps on getting diminished as one moves forward in time. So thus, even though even very old data points might have an effect on the RSI value, it would be very less.

So then, how many data points should one use, so that one can calculate a more or less correct value but its more convenient to do so.

The answer is, as many as possible. I mean mostly one would be calculating the values in excel, where calculating for 100 values or 10000 values is all the same. So, if you have the data, use all of it.

Problem arises when there is a scarcity of data. In that case i would aim to have 5 times data. 5 times of what ? While calculating RSI, one chooses to calculate it as a moving average of 'X' number of days, typically the number 14 is used. Thus I would prefer that i have atleast 14*5=70 days of data so that the calculation is accurate with an error rate of less than 0.5%