No—the British East India Company established a trading post in Singapore in 1613, but it was not burned down. Historical records indicate the post operated for a period before the British shifted their focus elsewhere in the region. The more famous founding of modern Singapore by Stamford Raffles occurred two centuries later, in 1819.
The 1613 settlement was a short-lived factory (trading outpost) and there's no evidence it was destroyed by fire. Any claims of its burning appear to be a conflation with later events or other locations.