Rabbi Akiva Eger's DNA?

Hello Samuel, Thanks for posing such an interesting question. I cannot give an absolute answer but I do not believe a dried blood sample remains viable for dna testing after nearly 200 years. A conclusive answer may require making an actual attempt using the actual sample. From what I know, only old bones are viable for dna extraction after so many years. Please further consult your question to a reputable dna testing laboratory.

It seems the DNA will only last about 10 years - https://academic.oup.com/ije/article/37/suppl_1/i7/665889