How long will this keep? Is it suitable for canning?

PS To answer the other part of your question - most chutneys last about a week to 10 days in the fridge. Some last longer. Check regularly and if no fuzzy growth or untoward smells, keep using it until gone.

Probably unsafe to can, as this chutney is both low acid and lacking sugar.
See national center for safe home preserving (maybe not exact title but close) website for more info.