In bash (4.3.46(1)) I have some multi-line so called fasta records where each record is initiated by on line with >name and the following lines DNA sequence ([AGCTNacgtn]),
With GNU grep:
grep -Pzo '>chr2\n[AGCTNacgtn\n]+' file | grep .
Output:
>chr2 TTGNACACCC TGGGGGAGTA