I carry mine in C&F fly boxes, I have 7 of these full with tubes in the bag, every one hooked and read to go
Personally I wouldn't like to put a hooked tubes in a plastic bag in my wading jacket pocket as it would end up looking like a tea bag
I now store them in cheap big lure boxes (like plano ones) that I carry in a bag that I leave on the bank.
I pick the ones I'd want at the end of the tippet before fishing a pool and put them even in a smaller box, or in ikea zipper bag that I've drilled with a punching press, or directly in the front pocket of the wader. There, surprisingly, they don't get damaged, especially the ones with feelers.
I've tried just about every box going but most have their faults. The Frodin wallets are OK for long winged flies but they do come out flat like angel fish Myran type boxes are fine for the car boot but if you do a bit of tramping about like me they become a tangled mess in the box. One of the best methods is one I pinched off McAndy on the forum, using XL plastic drinking straws. These can be sealed at one end and keep anything from long winged monkey type tubes to Francis tubes neat and tidy. I also use a couple of the boxes that use metal pins to hold the flies securely.
Been using the plastic drinking straws a few yrs now (posted about it at the time). You can get a lot more tubes in per compartment without any damage. For the very long flies I seal one end then keep the tubes protected on the inside of a length of pipe insulation (the grey stuff with a slit down the side). It prevents crush damage, doesn’t rattle about and is pocket friendly.
So I had a go at the marabou tubes in Oct '16 T&S. The results ended with a dilemma how to store said flies in one's box without it getting all mixed up and in a mess. So I firstly came up with sliding the fly into some spare shrink tubing I had in my tying box: This got me thinking...
I just use plano type boxes or the abu garcia lure boxes. Ill pick out 10 or so flies for the conditions on the day and stick them in one of these with hooks to suit. Ive got a second one with my pick of doubles etc.
Comp Lite Fly Boxes are constructed of tough, lightweight polypropylene with superior Easy-Slot Trout foam, in the lid that securely holds your flies without crushing or harming the delicate dressings.
The clear plastic holding the tubes is very flimsy and tubes can very easily fall out.