While backpacks have plenty of room ... Certain sling packs can hold fly fishing rods or rod tubes. It is more common for packs to have rod tube straps to carry an unrigged rod on long hikes.

There's not a ton of capacity here at just 3 L, so you'll only really be able to pack a fly box, phone, and a few spools of leader material in there. The Patagonia Guidewater 9L Hip Pack is another ...