First of all, I think this is a great idea. Like others on here, I am hugely wary of allowing access to my data. But I think if done right, and architected from the beginning with privacy and security in mind, there are huge opportunities to move beyond the antiquated receipt and loyalty systems currently used, whilst still respecting privacy. It sounds like you are starting from the perspective of doing this right, and respecting user privacy, rather than a quick, ill-considered grab to exploit users. And I’m more likely to trust an independent party than a large retailer for this kind of service, as I know the retailer ultimately just wants to sell me more goods.
Of course, I will remain sceptical until I see the final product and can read the policy, what I’m agreeing to, etc., but what I’ve read so far on this thread makes me very hopeful. Thanks for putting in the hard work – this aspect of banking is one I’m hugely keen to see progress on, and so far this is the first initiative that I’ve seen which has any promise (aside from any improvements Monzo will eventually provide natively, of course).
And thanks for gathering feedback early in your development process and being so responsive to what everyone has written. On to the specific questions you asked:
Ideally, I’d like more merchant details: phone number, opening hours, website and email. For online purchases, a link to the returns policy. It would be amazing if I need to go to the post office, and I could just look at the last transaction from my local Post Office and see what the opening hours are. Or need to return something to a shop, tap on the transaction for the item – or even just search for it, if the itemised receipt text is searchable – and see when the shop is open. Or if opening hours aren’t available, have a phone number there I can just tap to call.
I think listing warranty expiration date where appropriate would be great, too. For instance, if I bought a memory card that has a 2-year warranty, if I have a problem, I could search for it in Monzo, and the Flux receipt would not only show when I bought it, but when the warranty expires. I no longer have to search through the manufacturer’s website and figure out which warranty applies to my product, then hunt out the receipt to see when I bought it.
Being able to then export the receipt (as PDF) as a a proper proof-of-purchase that I can upload to a webform, or attach to an email, (as required by the warranty procedures) would be necessary. I already try and get rid of all paper receipts, scanning them in if no electronic copy is available to me. But some I have to keep as I’m not convinced my scan would be accepted in case of a warranty claim. Being certain that I don’t need the hard copy would be amazing, as would having all my receipts in Monzo.
However, I would also want the ability to export all my receipts (e.g. as individual PDFs) so I could store them myself if needed. Hard to imagine now ;-), but it’s conceivable that one day I might want to move away from Monzo, they close down current accounts, of they get bought by HSBC 
, etc. I don’t want my receipts held hostage. I think this goes back to some people’s concerns about who owns the data. Ultimately, these are my receipts, and I want to be able to do what I want with them.
I realise that I’ve strayed away from answering the question a bit, but I want to end this answer by saying that I think key to what you’re doing is that you don’t require me to enter my email address or any information with the retailer. There are some places I go that offer an email receipt (particularly independent cafés using iZettle POSes). But I can’t be bothered with entering my email address, and with larger (e.g. non-independent shops), I actually don’t want them having this information, as they’ll likely spam me. The great thing about contactless is how quick and frictionless it makes the payment side of things. From what I see, Flux continues to reduce the friction in the transaction process. Manually providing data to the merchant would obviously increase the friction, and is a retrograde step.
This is hugely valuable to me, in the way you’re talking about doing it – stamp cards. Because I don’t want retailers building up data on me and spamming me, I don’t use any of the chains’ loyalty schemes (e.g., ones where you are issued with a plastic card). If I did, my problem would actually be solved, as I use a great app called Stocard to store the few plastic cards I have (e.g. Library card, local shop that offers an early bird discount), so that I never have to carry the card around. However, what I do use are local cafés’ stamp card schemes (no data collection!).
The problem for me, is that I like a very thin wallet (3 cards and cash) and don’t want to crowd my pocket with loads of pieces of cardboard. I don’t go to cafés daily, and there are only one or two that I go to regularly enough to make it worth always having the stamp card on me. However, over a month, I will go into several others at least once. Inevitably this tends to be spur-of-the-moment/opportunistic, so I’ve left the stamp card at home. I either loose out on the stamp, or get a new one and then have to later consolidate six cards with one or two stamps each. I find the whole thing a bit of a hassle, and generally just forgo the stamps except for at 2-3 places. I understand why the cafés use stamp cards. They are incredibly cheap to implement, and they don’t want huge overheads for a loyalty scheme. If you could solve the problem in a way that is financially viable for small cafés, that would be amazing. I’m really unconcerned about the big loyalty schemes (Tesco, Costa, Boots, etc.).
I don’t have a problem with your example of offering Alice’s Café’s new chicken wrap because I normally order the chicken sandwich. But I also think it’s a bit of a contrived example. If we’re talking about an independent café which I frequent, it’s incredibly unlikely I wouldn’t notice a menu change. Even if it’s a chain café/restaurant which I frequent, I’m sure I would notice a menu change, and those places normally blast it in your face whenever they have something new to offer. 
So I’m not sure there’s much value to add there.
I think something more sophisticated might be interesting. Say, I’m in a different town, or a part of town I don’t go to frequently, I would find it very useful to find places nearby that I’m likely to like. If I’m in an unfamiliar area and I could go to a transaction from my local coffee shop and tap a button that says, “Find places like this near me”, and Flux would recommend a local coffee shop with similar qualities (e.g. specialty coffee and homemade cakes, or the nearest Costa, depending on what profile the coffee shop in the transaction has), that would be fantastic.
Randomly popping up ‘deals’ or ‘things I might want’ is not something I’m interested in. I’ve no problem with your including this in Flux, as long as: (1) I can turn it off; (2) it’s clear that my privacy interests are being looked after.
I would like an option to automatically email me a PDF copy of the receipt. Ideally I can set a default, but also override it and turn the option on and off for particular merchants. For instance, I want to automatically receive an emailed receipt every time I shop at Argos, get a train ticket, etc., but I definitely don’t want one every time I go to my local coffee shop, buy a sandwich, etc. This should be done through the email address already registered with Monzo, ideally you wouldn’t even know what that address is. You just tell Monzo to email me the PDF receipt. That way, the receipt comes through as ‘official’ Monzo email (helps with email filters, automation, etc.). But however it’s done, going back to part of my answer to Q1, I would like the ability to automatically keep my receipts independently of the Monzo app.
Finally, your plan to start on a concentrated area to provide maximum coverage, and then expand, sounds smart. I imagine you’re thinking of somewhere in London, but can I suggest that Edinburgh would be a great place to start. 
We have a vibrant community of shops and cafés, it’s a small city, so manageable, and you could get loads of publicity during the many festivals in the city. 