BGP is a routing protocol that is mostly used for propagating routing/reachability information that also includes additional data that can be used (communities as tags, etc).
A few years ago folks wanted to bake in additional functionality. For example, packet filters (aka ACLs) normally are deployed to router configuration files using each operators own tooling. To deploy this against hundreds or thousands of routers rapidly was a challenge for them (not good at swdev, etc.). So the idea was we already have a protocol that propagates state to every router rapidly in the network, let's find a way to bake ACLs into the BGP updates.
The result wasnt that good for a few reasons:
1) bgp state isn't sticky. If a router goes offline or bgp sessions reset, acls go away. That means if you are using flowspec for a critical need like always on packet filters you've got the wrong tool.
2) the implementation had various bugs.
3) most importantly it gave people a really easy way to hurt themselves globally. There was no phased deployment with pre and post checks. What you deployed led to packet filters being installed across the network in seconds. In most cases (depends on your config) the only way to remove it is remove the specific flowspec route or have bgp reset to it.
I've seen bad flowspec routes core dump the daemon on a router responsible for programming ACLs that led to them being unable to withdraw the programmed entry. I've seen as bugs on tcp/UDP port matches go wrong and eat lot more than intended. I've seen so many flowspec rules installed on a network where it exhausted routers ability to inspect and process packets and you'd see flat lining of packets being dropped.
In my opinion, it's a hack around not having a good ACL deployment tool that has led to many outages in its wake.
Edit: another flowspec gotcha. Some folks like to integrate ddos tooling systems into flowspec. An example of this is if I run a network and some IP address behind me gets lit up, deploy a rule for that specific IP and rate limit traffic to it. Unfortunately, sometimes folks don't put a lot of care into making sure it can't mess with internal IPs that should be off limits. Like route reflectors, router loopback IPs, etc. I've seen situations where some networks have had a bad day due to a ddos or traffic mis classified as ddos by auto installing rules to protect something but actually impair legitimate communications to network infrastructure which then causes the outage.
Also, flowspec doesn't work like regular ACLs where you have input and output on a per interface basis - it applies to all traffic traversing a router, which makes it difficult to say which interfaces should be exempt (think internal vs external).