faSplit from Jim Kent's tools. Link for linux version. chmod a+x faSplit after download.

faSplit - Split an fa file into several files.
usage:
   faSplit how input.fa count outRoot
where how is either 'about' 'byname' 'base' 'gap' 'sequence' or 'size'.  
Files split by sequence will be broken at the nearest fa record boundary. 
Files split by base will be broken at any base.  
Files broken by size will be broken every count bases.

For what you want

faSplit size input.fa 1000 outRoot

This breaks up input.fa into 1000 base chunks

We use seqkit to slide on sequences with 1kb window:

seqkit sliding -s 1000 -W 1000 seqs.fa.gz -o out.fa.gz

You can also adjust step size to make interleaved chunks in some scenarios, e.g., -s 900 -W 1000 for 1kb fragments with 100bp overlap.

Usage and examples:

sliding sequences, circular genome supported

Usage:
  seqkit sliding [flags]

Flags:
  -C, --circular-genome   circular genome.
  -g, --greedy            greedy mode, i.e., exporting last subsequences even shorter than windows size
  -s, --step int          step size
  -W, --window int        window size

Plenty of solution described here : Tutorial: FASTA file split

Use shred.sh from BBMap suite.

Usage:  shred.sh in=<file> out=<file> length=<number> minlength=<number> overlap=<number>

in=<file>       Input sequences.
out=<file>      Destination of output shreds.
length=500      Desired length of shreds.
minlength=1     Shortest allowed shred.  The last shred of each input sequence may be shorter than desired length.
overlap=0       Amount of overlap between successive reads.