There are around 15,000 flowering plant species in India. However, an another report has mention of more than 18000 species of flowering plants , accounting for more than 7 percent of the total plant species of the world. You can find varying figures in different reports through web search.
For Indian region a critical study is still not there. At JNTBGRI, when we compiled the published literature for Flora of Kerala State and also for Flora of the Western Ghats, the actual number was 1500 to 2000 species above what we found in the existing reports and papers. This increase we may expect in the case of Indian flora also.
No any data is available till date about the exact number of flowering plants in India. However, according to an estimate the number of flowering plants in India ranges between 15,000 to 20,000.