Whether or not a Flexi Season is the cheapest option very much depends on the journey you're making, the times of day you'll be travelling and whether or not you are eligible for a Railcard.
On the latter point, I take it that you are aged 30-59 and not eligible for the Veterans, Disabled etc. Railcard? You would of course still be eligible for region-based Railcards such as the Network Railcard or (indirectly) the Gold Card, which may make your commute cheaper. It's also possible that there might be Advance tickets you could use if you're prepared to tie yourself to specific services.
If none of these avenues assist and a Flexi Season really is the cheapest option, I believe it is currently advantageous to buy season tickets from LNER. Several card issuers have offers of 5% cashback for LNER purchases, which seemingly include season tickets (even though this must mean they are making a significant loss on each one sold - as the commission is well under 5% for seasons). Some of these offers only include in-person purchases so you might need to make your way to an LNER Travel Centre, though I presume that wouldn't be too much of a hassle as there's one at Kings Cross if nothing else.
In terms of the card you use, you'll almost certainly be wanting to use an Amex card of whatever type is most suitable for your particular circumstances. There are lots of signup offers available if you can spend a certain amount within X months, often increased if you obtain a referral from an existing customer.
