sry for the late replay, you can use the flowmap for 2d animation but you will need a shader to do so

for the tool the following shader was used:

Code:
Shader "Custom/WaterFlow" {
        Properties {
                _MainTex ("Base (RGB)", 2D) = "white" {}
                _Noise ("Noise", 2D) = "white" {}
                //_TexBlend ("Texture", 2D) = "white" {}
                _FlowSpeed ("Flow Speed", Float) = 1
                _Tiling ("Tiling", Float) = 1
                _PanX ("Panning X", Float) = 0
                _PanY ("Panning Y", Float) = 0
        }
        SubShader {
                Tags { "RenderType"="Opaque" }
                LOD 200
                
                CGPROGRAM
                #pragma surface surf Lambert

                sampler2D _MainTex;
                sampler2D _Noise;
                //sampler2D _TexBlend;
                float _FlowSpeed;
                float _Tiling;
                float _PanX;
                float _PanY;

                struct Input {
                        float2 uv_MainTex;
                        float4 color : COLOR;
                };

                void surf (Input IN, inout SurfaceOutput o) {
                        half4 noise = tex2D(_Noise, IN.uv_MainTex);
                        half2 distortion = (IN.color.rg * 2 - 1);
                        half time = _Time.x * _FlowSpeed;
                        half2 panning = half2(_PanX, _PanY) * time;
                        half4 c1 = tex2D (_MainTex, IN.uv_MainTex * _Tiling + panning + distortion * fmod(time, 1));
                        half4 c2 = tex2D (_MainTex, IN.uv_MainTex * _Tiling + panning + distortion * fmod(time + 0.5, 1));
                        //half4 c3 = tex2D (_TexBlend, IN.uv_MainTex * _Tiling);
                        half4 c = lerp(c1, c2, abs(0.5 - fmod(time, 1)) / 0.5);
                        //c = lerp(c, c3, IN.color.B);
                        o.Albedo = c.rgb;
                        o.Alpha = c.a;
                }
                ENDCG
        } 
        FallBack "Diffuse"
}
note: this shader is basicly for unity but you will find some more on the internet or make your own