Epic fight mod is not compatible with this how can i make it compatible?

I had the same problem
its "more" on the epic fight side
went to the epicfight-client.toml
set "filter_animation = true"
now you get the normal flying animation in moving mode (normal) and a very cool flying battle animation in battle mode
(I also recomend to set all items in "mining_autoswitch_items" and battle_autoswitch_items)

only, the first person view while flying in battle mode is a little messed up, its using the normal wings view, but the resulst from both mods is epic. it just has to check if epic fights battle is enabled to change the camera.
I give you an example https://cdn.discordapp.com/attachments/847998484946354177/960218185775349830/wingsandepicfight.gif

and for KYSCollision,
if you like epic fight you could like parcool too. after some setting its also compatible.

Is there any other way to stop having the normal walking animation and fly with it? It's really bugging me when I don't want to be in attack mode where I see others walking default.

you can get the source code and patch it yourself, if you can. also reporting to both developers and wait.
the easiest way are the configs I mentioned above.
set "filter_animation = true" in the epicfight-client.toml open it with notepad/np++
set all items and blocks that arn't weapons (including air) to auto switch into normal mode.
now just dont fly with a weapon in your main hand if you are in first person. you could try to autoswitch the perspective as well if you are holding a weapon.
the last other option, you have to decide, except it, or only use one of them. epicfight or wings.