if you have extracted DNA, you can use PCR primers specific for the mtDNA or cpDNA and sequence the amplified products.
if you still have the tissue, you could do some organelle isolation, but it difficult to obtain pure samples. We have done that on the mtDNA of a fungi:
Article Quantification of Neurospora crassa mitochondrial DNA using ...
Do you have the whole genome sequencing data now? If you have WGS data, especially third-generation sequencing data, you can assemble the chloroplast and mitochondrial genomes by bioinformatic methods. In that case, you do not need to isolate organelle DNA by means of traditional experiments.
We have a lot of experience in assembling organelle genomes by bioinformatic methods, and here is our latest paper, which you can refer to: