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Unfortunately, I am not aware of a Sinhala translation of the Tripitaka that is available in a Kindle-friendly format. The Buddha Jayanti Tripitaka Series is a landmark translation of the Pali Tipitaka into Sinhala, but it was published in print format only as far as I know.
Some options you could consider:
Convert the PDF files to Kindle format using an online conversion tool or Calibre. The formatting may not be perfect, but it should be readable.
See if any individual suttas or books from the Buddha Jayanti series are available in Kindle format. Some may have been converted already.
Consider an English translation like the Pali Text Society editions. These are available legally for purchase in Kindle format. An English translation may be preferable for study purposes anyway.
Access the Buddha Jayanti books on a tablet or large smartphone. The PDFs should display well on those devices even if not optimized for Kindle.
I know the Buddha Jayanti books hold a special place for Sinhala Buddhists. Hopefully they will become more accessible digitally in the future to reach new generations of readers. But for now Kindle support seems limited unfortunately.