Leontief's Paradox and the amount of capital Leontief (1953) showed that US exports in 1947 embodied considerably less capital and somewhat more labor than would be required for domestic production of competitive imports. \$2.55 million worth of capital was used to produce \$1 million (against $3.1 million for "imports"). What is being measured here is the total capital stock which I guess exceeds that part of the capital stock that was used to produce exports that year. 

Would it be more appropriate to measure the capital used that year by the depreciation on the total stock? Is there any reference on this?
Leontief did not use total capital stock for his calculation of capital/labor requirements in the export/import sector. He measured 'requirements per million dollars of exports and imports replacements', and this for various industries (Leontief, 1953, section III, table 2). So he also did not use total capital stock, he used capital requirements AKA capital inputs. 

He did provide summary statistics on the total capital and labor required per million dollars of total output for each industry. This might have confused you. 

Note that he obtained these numbers only after computing them from available data, and he discusses their accuracy in the same section.